ICSE

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 28 Polygons

Polygons Exercise 28A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
State, which of the following are polygons :

Solution:

Question 2.
Find the sum of interior angles of a polygon with :
(i) 9 sides
(ii) 13 sides
(iii) 16 sides
Solution:

Question 3.
Find the number of sides of a polygon, if the sum of its interior angles is :
(i) 1440°
(ii) 1620°
Solution:

Question 4.
Is it possible to have a polygon, whose sum of interior angles is 1030°.
Solution:

Question 5.
(i) If all the angles of a hexagon arc equal, find the measure of each angle.
(ii) If all the angles of an octagon are equal, find the measure of each angle,
Solution:

Question 6.
One angle of a quadrilateral is 90° and all other angles are equal ; find each equal angle.
Solution:

Question 7.
If angles of quadrilateral are in the ratio 4 : 5 : 3 : 6 ; find each angle of the quadrilateral.
Solution:

Question 8.
If one angle of a pentagon is 120° and each of the remaining four angles is x°, find the magnitude of x.
Solution:

Question 9.
The angles of a pentagon are in the ratio 5 : 4 : 5 : 7 : 6 ; find each angle of the pentagon.
Solution:
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Question 10.
Two angles of a hexagon are 90° and 110°. If the remaining four angles arc equal, find each equal angle.
Solution:

Polygons Exercise 28B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
In case of regular polygon, with

Solution:

Question 2.
Find the number of sides in a regular polygon, if its each interior angle is :
(i) 160°
(ii) 150°
Solution:

Question 3.
Find number of sides in a regular polygon, if its each exterior angle is :
(i) 30°
(ii) 36°
Solution:

Question 4.
Is it possible to have a regular polygon whose each interior angle is :
(i) 135°
(ii) 155°
Solution:

Question 5.
Is it possible to have a regular polygon whose each exterior angle is :
(i) 100°
(ii) 36°
Solution:

Question 6.
The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :
(i) each exterior angle of this polygon.
(ii) number of sides in the polygon.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Quadrilateral Exercise 27A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:

Question 3.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x-20)° and 6(x+3)°. Find
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C

Solution:

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD.
Solution:

Question 6.
From the following figure find ;
(i) x,
(ii) ∠ABC,
(iii) ∠ACD.
Solution:

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ;
∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
Solution:

Question 8.
In the given figure :
∠b = 2a + 15
and ∠c = 3a+5; find the values of b and c.

Solution:

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other. Is PS also parallel to QR ?
Solution:

Question 11.
Use the information given in the following figure to find the value of x.
Solution:

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel.
If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Solution:

Quadrilateral Exercise 27B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.
Solution:

Question 2.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Solution:

Question 3.
The angles A, B, C and D of a trapezium ABCD are in the ratio 3 : 4 : 5 : 6.
Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer
Solution:

Question 4.
In an isosceles trapezium one pair of opposite sides are ….. to each Other and the other pair of opposite sides are ….. to each other.
Solution:

Question 5.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
Solution:
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Question 6.
Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.
Solution:

Question 7.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Solution:

Question 8.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
Solution:

Question 9.
The angles A, B, C and D of a quadrilateral are in the ratio 2:3: 2 : 3. Show this quadrilateral is a parallelogram.
Solution:

Question 10.
In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.

If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.
Solution:

Question 11.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.

Solution:

Question 12.
In parallelogram ABCD, ∠A = 90°
(i) What is the measure of angle B.
(ii) Write the special name of the paralleogram.
Solution:

Question 13.
One diagnol of a rectangle is 18 cm. What is the length of its other diagnol?
Solution:

Question 14.
Each angle of a quadrilateral is x + 5°. Find :
(i) the value of x
(ii) each angle of the quadrilateral.
Give the special name of the quadrilateral taken.

Solution:

Question 15.
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Solution:

Question 16.
The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.
Solution:

Question 17.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.

Solution:

Question 18.
Write two conditions that will make the adjoining figure a square.

Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

Triangles Exercise 26A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In each of the following, find the marked unknown angles :


Solution:

Question 2.
Can a triangle together have the following angles ?
(i) 55°, 55° and 80°
(ii) 33°, 74° and 73°
(iii) 85°, 95° and 22°.
Solution:

Question 3.
Find x, if the angles of a triangle are:
(i) x°, x°, x°
(ii) x°, 2x°, 2x°
(iii) 2x°, 4x°, 6x°
Solution:

Question 4.
One angle of a right-angled triangle is 70°. Find the other acute angle.
Solution:

Question 5.
In ∆ABC, ∠A = ∠B = 62° ; find ∠C.
Solution:

Question 6.
In ∆ABC, C = 56°C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.
Solution:

Question 7.
Find, giving reasons, the unknown marked angles, in each triangle drawn below:


Solution:

Question 8.
Classify the following triangles according to angle :


Solution:

Question 9.
Classify the following triangles according to sides :

Solution:

Triangles Exercise 26B – Selina Concise Mathematics Class 6 ICSE Solutions

Construct traingle ABC, when :
Question 1.
AB = 6 cm, BC = 8 cm and AC = 4 cm.
Solution:

Question 2.
AB = 3.5 cm, AC = 4.8 cm and BC = 5.2 cm.
Solution:

Question 3.
AB = BC = 5 cm and AC = 3 cm. Mea¬sure angles A and C. Is ∠A = ∠C?
Solution:

Question 4.
AB = BC = CA = 4.5 cm. Measure all the angles of the triangle. Are they equal ?
Solution:

Question 5.
AB = 3 cm, BC = 7 cm and ∠B = 90°.
Solution:

Question 6.
AC = 4.5 cm, BC = 6 cm and ∠C = 60°.
Solution:

Question 7.
AC = 6 cm, ∠A = 60“ and ∠C = 45°. Measure AB and BC.
Solution:

Question 8.
AB = 5.4 cm, ∠A = 30° and ∠B = 90°. Measure ∠C and side BC.
Solution:

Question 9.
AB = 7 cm, ∠B = 120° and ∠A = 30°. Measure AC and BC.
Solution:

Question 10.
BC = 3 cm, AC = 4 cm and AB = 5 cm. Measure angle ACB. Give a special name to this triangle.
Solution:

Triangles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
If each of the two equal angles of an isosceles triangle is 68°, find the third angle.
Solution:

Question 2.
One of the angles of a triangle is 110°, the two other angles are equal. Find their value.
Solution:

Question 3.
The angles of a triangle are in the ratio 3:5: 7. Find each angle.
Solution:

Question 4.
The angles of a triangle are (2x – 30°),(3x – 40°) and (\(\frac { 5 }{ 2 }\)x + 10°) Find the value of x .
Solution:

Question 5.
In each of the following figures, triangle ABC is equilateral and triangle PBC is isosceles. If PBA = 20°; find in each case:
(a) angle PBC.
(b) angle BPC.

Solution:

Question 6.
Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.
Solution:

Question 7.
Construct a triangle PQR, given PQ = 6 cm, ∠P = 60° and ∠Q = 30°. Measure angle R and the length of PR.
Solution:

Question 8.
Construct a triangle ABC given BC = 5 cm, AC = 6 cm and ∠C = 75°. Draw the bisector of the interior angle at A. Let this bisector meet BC at P ; measure BP.
Solution:

Question 9.
Using ruler and a pair compass only, construct a triangle XYZ given YZ = 7 cm, ∠XYZ = 60° and ∠XZY = 45°. Draw the bisectors of angles X and Y.
Solution:

Question 10.
Using ruler and a pair compass only, construct a triangle PQR, given PQ = 5.5 cm, QR = 7.5 cm and RP = 6 cm. Draw the bisectors of the interior angles at P, Q and R. Do these bisectors meet at the same point ?
Solution:

Question 11.
One angle of a triangle is 80° and the other two are in the ratio 3 : 2. Find the unknown angles of the triangle.
Solution:

Question 12.
Find the value of x if ∠A = 32°, ∠B = 55° and obtuse angle AED = 115°.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 9 Profit, Loss and Discount

Profit, Loss and Discount Exercise 9A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the gain or loss percent, if
(i) C.P. = Rs. 200 and S.P.: = Rs. 224
(ii) C.P. = Rs. 450 and S.P. = Rs. 400
(iii) C.P. = Rs. 550 and gain = Rs . 22
(iv) CP. = Rs. 216 and loss = Rs. 72
(v) S.P. = Rs. 500 and loss : = Rs. 100
(vi) S.P. = Rs. 12 and profit = Rs. 4
(vii) C.P. = Rs. 5 and gain = 60 P

Solution:

Question 2.
Find the selling price, if:
(i) C.P. = Rs. 500 and gain = 25%
(ii) C.P. = Rs. 60 and loss = 12 1/2%
(iii) C.P. = Rs. 150 and loss = 20%
(iv) C.P. = Rs. 80 and gain = 2.5%
Solution:

Question 3.
Rohit bought a tape-recorder for Rs. 1,500 and sold it for Rs. 1,800. Calculate his profit or loss percent.
Solution:

Question 4.
An article bought for Rs. 350 is sold at a profit of 20%. Find its selling price.
Solution:

Question 5.
An old machine is bought for Rs. 1,400 and is sold at a loss of 15%. Find its selling price.
Solution:

Question 6.
Oranges are bought at 5 for Rs. 10 and sold at 6 for Rs. 15. Find profit or loss as percent.
Solution:

Question 7.
A certain number of articles are bought at 3 for Rs. 150 and all of them are sold at 4 for Rs. 180. Find the loss or gain as percent.
Solution:

Question 8.
A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.
Solution:

Question 9.
The cost price of an article is Rs. 1,200 and selling price is \(\frac { 5 }{ 4 }\) times of its cost price. Find:
(i) selling price of the article
(ii) profit or loss as percent.
Solution:

Question 10.
The selling price of an article is Rs. 1,200 and cost price is \(\frac { 5 }{ 4 }\) times of its selling price,
find :
(i) cost price of the article ;
(ii) profit or loss as percent.
Solution:

Profit, Loss and Discount Exercise 9B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the cost price, if:
(i) S.P. = Rs. 21 and gain = 5%
(ii) S.P. = Rs. 22 and loss = 12%
(iii) S.P. = Rs. 340 and gain = Rs. 20
(iv) S.P. = Rs. 200 and loss = Rs. 50
(v) S.P. = Re. 1 and loss = 5 p.
Solution:

Question 2.
By selling an article for Rs. 810, a loss of 10 percent is suffered. Find its cost price.
Solution:

Question 3.
By selling a scooter for Rs. 9,200, a man gains 15%. Find the cost price of the scooter.
Solution:

Question 4.
On selling an article for Rs. 2,640, a profit of 10 percent is made. Find
(i) cost price of the article
(ii) new selling price of it, in order to gain 15%
Solution:

Question 5.
A T.V. set is sold for Rs. 6800 at a loss of 15%. Find
(i)cost price of the T.V. set.
(ii)new selling price of it, in order to gain 12%
Solution:

Question 6.
A fruit seller bought mangoes at Rs. 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for.
(i) one mango
(ii) 40 mangoes
Solution:

Question 7.
By selling two transistors for Rs. 00 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other.
Find :
(i) C.P. of each transistor
(ii) total C.P. and total S.P. of both the transistors
(iii) profit or loss percent on the whole.
Solution:

Question 8.
Mangoes are bought at 20 for Rs. 60. If
they are sold at 33\(\frac { 1 }{ 3 }\) percent profit.
Find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Solution:

Question 9.
Find the cost price of an article, which is sold for Rs. 4050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Solution:

Question 10.
By selling an article for ₹825, a man loses \(\frac { 1 }{ 3 }\) equal to j of its selling price.
Find :
(i) the cost price of the article,
(ii) the profit percent or the loss percent made, if the same article is sold for ₹1265.
Solution:

Question 11.
Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles.
Solution:

Question 12.
Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.
Solution:

Question 13.
The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Solution:

Question 14.
The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Solution:

Question 15.
Hundred oranges are bought for ₹350 and all of them are sold at the rate of ₹48 per dozen. Find the profit percent or loss percent made.
Solution:

Question 16.
Oranges are bought at 100 for ?80 and all of them are sold at ₹80 for ₹100. Find the loss or gain as percent in this transaction.
Solution:

Question 17.
An article is bought for ₹5,700 and ₹1,300 is spent on its repairing, transportion, etc. For how much should this article be sold in order to gain 20% on the whole.
Solution:
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Profit, Loss and Discount Exercise 9C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A machine is marked at ₹5000 and is sold at a discount of 10%. Find the selling price of the machine.
Solution:

Question 2.
shopkeeper marked a dinner set for ₹1000. He sold it at ₹900, what percent discount did he give ?
Solution:

Question 3.
A pair of shoes marked at ₹320, are sold at a discount of 15 percent.
Find :
(i) discount
(ii) selling price of the shoes.
Solution:

Question 4.
The list price of an article is ₹450 and it is sold for ₹360.
Find :
(i) discount
(ii) discount percent
Solution:

Question 5.
A shopkeeper buys an article for₹300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Solution:

Question 6.
A car is marked at Rs. 50,000. The dealer gives 5% discount on first Rs. 20,000 and 2% discount on the remaining Rs. 30,000.
Find :
(i) the total discount.
(ii) the price charged by the dealer.
Solution:

Question 7.
A dealer buys a T.V. set for Rs. 2500. He marks it at Rs. 3,200 and then gives a discount of 10% on it.
Find :
(i) the selling price of the T.V. set
(ii) the profit percent made by the dealer.
Solution:

Question 8.
A sells his goods at 15% discount. Find the price of an article which is sold for Rs. 680.
Solution:

Question 9.
A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges Rs. 560.
Solution:

Question 10.
An article is bought for Rs. 1,200 and Rs. 100 is spent on its transportation, etc.
Find :
(i) the total C.P. of the article.
(ii) the selling price of it in order to gain 20% on the whole.
Solution:

Question 11.
40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 80
Find :
(i) C.P. of one pen.
(ii) S/P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens. Are the results of parts (iv) and (viii) same? What conclusion do you draw from the above result ?
Solution:

Question 12.
The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought are sold.
Solution:

Question 13.
The C.P. of 8 pens is same as S.P. of 10 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold
Solution:

Question 14.
A certain number of articles are bought at Rs. 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:
(i) one article
(ii)seven articles.
Solution:

Question 15.
An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 25 Properties of Angles and Lines (Including Parallel Lines)

Properties of Angles and Lines Exercise 25A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find :
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC

Solution:

Question 2.
The adjoining figure, shows two straight lines AB and CD intersecting at point P. If ∠BPC = 4x – 5° and ∠APD = 3x + 15° ; find :

(i) the value of x.
(ii) ∠APD
(iii) ∠BPD
(iv) ∠BPC
Solution:

Question 3.
The given diagram, shows two adjacent angles AOB and AOC, whose exterior sides are along the same straight line. Find the value of x.

Solution:

Question 4.
Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.


Solution:

Question 5.
A line segment AP stands at point P of a straight line BC such that ∠APB = 5x – 40° and ∠APC = .x+ 10°; find the value of x and angle APB.
Solution:

Properties of Angles and Lines Exercise 25B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Identify the pair of angles in each of the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.


Solution:

Question 2.
Each figure given below shows a pair of parallel lines cut by a transversal For each case, find a and b, giving reasons.




Solution:

Question 3.
If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.

Solution:

Question 4.
In the figure given below, find the measure of the angles denoted by x,y, z,p,q and r.

Solution:

Question 5.
Using the given figure, fill in the blanks.

Solution:

Question 6.
In the given figure, find the anlges shown by x,y, z and w. Give reasons.

Solution:

Question 7.
Find a, b, c and d in the figure given below :

Solution:

Question 8.
Find x, y and z in the figure given below :

Solution:

Properties of Angles and Lines Exercise 25C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In your note-book copy the following angles using ruler and a pair compass only.

Solution:

Question 2.
Construct the following angles, using ruler and a pair of compass only
(i) 60°
(ii) 90°
(iii) 45°
(iv) 30°
(v) 120°
(vi) 135°
(vii) 15°
Solution:

Question 3.
Draw line AB = 6cm. Construct angle ABC = 60°. Then draw the bisector of angle ABC.
Solution:

Question 4.
Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths of PR and QR. Is PR = QR ?
Solution:

Question 5.
Draw a line segment AB = 7cm. Mark a point Pon AB such that AP=3 cm. Draw perpendicular on to AB at point P.
Solution:

Question 6.
Draw a line segment AB = 6.5 cm. Locate a point P that is 5 cm from A and 4.6 cm from B. Through the point P, draw a perpendicular on to the line segment AB.
Solution:

Properties of Angles and Lines Exercise 25D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Draw a line segment OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B ; then measure the length ofAB.
Solution:

Question 2.
Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.
Solution:

Question 3.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses. Measure each angle so obtained and check whether or not the new angles obtained on bisecting ∠ABC are equal.
Solution:

Question 4.
Draw ∠PQR = 75° by using set- squares. On PQ mark a point M such that MQ = 3 cm. On QR mark a point N such that QN = 4 cm. Join M and N. Measure the length of MN.
Solution:

Properties of Angles and Lines Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In the following figures, AB is parallel to CD; find the values of angles x, y and z :

Solution:

Question 2.
In each of the following figures, BA is parallel to CD. Find the angles a, b and c:

Solution:

Question 3.
In each of the following figures, PQ is parallel to RS. Find the angles a, b and c:

Solution:

Question 4.
Two straight lines are cut by a transversal. Are the corresponding angles always equal?
Solution:

Question 5.
Two straight lines are cut by a transversal so that the co-interior angles are supplementary. Are the straight lines parallel?
Solution:

Question 6.
Two straight lines are cut by a transversal so that the co-interior angles are equal. What must be the measure of each interior angle to make the straight lines parallel to each other ?
Solution:

Question 7.
In each case given below, find the value of x so that POQ is straight line


Solution:

Question 8.
in each case, given below, draw perpendicular to AB from an exterior point P

Solution:

Question 9.
Draw a line segment BC = 8 cm. Using set-squares, draw ∠CBA = 60° and ∠BCA = 75°. Measure the angle BAC. Also measure the lengths of AB and AC.
Solution:

Question 10.
Draw a line AB = 9 cm. Mark a point P in AB such that AP=5 cm. Through P draw (using set-square) perpendicular PQ = 3 cm. Measure BQ.
Solution:

Question 11.
Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.
Solution:

Question 12.
Without using set squares, construct angle ABC = 60° in which AB = BC = 5 cm. Join A and C and measure the length of AC.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions