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ML Aggarwal Class 7 Solutions Chapter 10 Lines and Angles Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 10 Lines and Angles Check Your Progress

Question 1.
Find the supplementary angle of each of the following angles:
(i) \(\frac { 1 }{ 2 }\) of 90°
(ii) \(\frac { 3 }{ 7 }\) of 280°
Solution:

Question 2.
How many degrees are there in an angle which is one-fifth of its complement?
Solution:

Question 3.
If two angles are supplementary and one angle is 5° more than four times the other, find the angles.
Solution:

Question 4.
The given diagram shows two intersecting straight lines. Find the values of x, y and z.

Solution:

Question 5.
In the given diagram, lines AB and CD intersect at O. If ∠1 + ∠3 = 78°, find the size of ∠2.

Solution:

Question 6.
(a) In the figure (i) given below, l || m. If ∠5 = 65°, find all other angles.
(b) In the figure (ii) given below, l || m. Find the values of x, y and z.
(c) In the figure (iii) given below, l || m and p || q. Find the values of x, y and z.

Solution:

ML Aggarwal Class 7 Solutions Chapter 10 Lines and Angles Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 10 Lines and Angles Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is ………..
(ii) If two angles are supplementary, then the sum of their measures is …………
(iii) Supplement of an obtuse angle is ……….
(iv) Two angles forming a linear pair are ……….
(v) If two adjacent angles are supplementary, then they form a ………..
(vi) Angles of a linear pair are as well as ………..
(vii) Adjacent angles have a common vertex, a common ……….. and no common ………
(viii)Angles formed by two intersecting lines having no common arms are called ………..
(ix) If two lines intersect and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are ……..
(x) Two lines in a plane which never meet are called ……….
(xi) Alternate interior angles have one common …………
(xii) Corresponding angles are on the ……….. side of the transversal.
(xiii) Alternate interior angles are on the ………… side of the transversal.
(xiv) If two lines are cut by a transversal such that a pair of corresponding angles are not equal, then the lines are ………..
Solution:

Question 2.
In the given figure, AB is a straight line and OD ⊥ AB. Observe the figure and fill in the following blanks:

(i) ∠AOC and ∠COE form a pair of ……….. angles.
(ii) ∠AOC and ∠COB are ……….. angles.
(iii) ∠AOC is ………… of ∠COD.
(iv) ∠BOE is …………. of ∠EOA.
Solution:

Question 3.
State whether the following statements are true (T) or false (F):
(i) Two obtuse angles can be supplementary.
(ii) Two acute angles can form a linear pair.
(iii) Two obtuse angles can form a linear pair.
(iv) Two adjacent angles always form a linear pair.
(v) Pair of vertically opposite angles are always supplementary.
(vi) 30° is one-half of its complement.
(vii) If two lines are cut by a transversal,
then each pair of corresponding angles are equal.
(viii) If two lines are cut by a transversal,
then each pair of alternate interior angles are equal.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (4 to 14):
Question 4.
A pair of complementary angles is
(a) 130°, 50°
(b) 35°, 55°
(c) 25°, 75°
(d) 27°, 53°
Solution:

Question 5.
A pair of supplementary angles is
(a) 55°, 115°
(b) 65°, 125°
(b) 47°, 133°
(d) 40°, 50°
Solution:

Question 6.
If an angle is one-third of its supplement, then the measure of the angle is
(a) 45°
(b) 30°
(c) 135°
(d) 150°
Solution:

Question 7.
If an angle measures 10° more than its complement, then the measure of the angle is
(a) 40°
(b) 55°
(c) 35°
(d) 50°
Solution:

Question 8.
If one angle of a linear pair is acute, then the other angle is
(a) acute
(b) obtuse
(c) right
(d) straight
Solution:

Question 9.
In the given figure, the value of x that will make AOB a straight line is
(a) x = 40
(b) x = 35
(c) x = 30
(d) x = 25

Solution:

Question 10.
If two lines are intersected by a transversal, then the number of pairs of interior angles on the same side of transversal is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Question 11.
In the given figure, if l || m then the value of x is
(a) x = 50
(b) x = 60
(c) x = 70
(d) x = 45

Solution:

Question 12.
In the gitsen figure, if l || m then the value of x is
(a) x = 75°
(b) x = 95°
(c) x = 105°
(d) x = 115°

Solution:

Question 13.
In the given figure, AB || CD. If ∠APQ = 50° and ∠PRD = 130°, then ∠QPR is
(a) 30°
(b) 50°
(c) 80°
(d) 130°

Solution:

Question 14.
In the given figure, PA || BC || DQ and AB || DC. Then the values of x and y are respectively:
(a) 50°, 120°
(b) 50°, 130°
(c) 60°, 120°
(d) 60°, 130°

Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
Calculate the measure of each lettered angle in the following figures (parallel line segments / rays are denoted by thick matching arrows):

Solution:

ML Aggarwal Class 7 Solutions Chapter 10 Lines and Angles Ex 10.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 10 Lines and Angles Ex 10.2

Question 1.
Identify each of the given pair of angles as alternate interior angles, co-interior angles or corresponding angles or none of these in the given figure:

(i) ∠2, ∠6
(ii) ∠1, ∠6
(iii) ∠3, ∠5
(iv) ∠2, ∠7
(v) ∠3, ∠6
(vi) ∠4, ∠8
Solution:

Question 2.
State the property that is used in each of the following statements:
(i) If a || b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a || b.
(iii) If ∠4 + ∠5 = 180°, then a || b.

Solution:

Question 3.
In each of the following figures, a pair of parallel lines is cut by a transversal. Find the value of x:

Solution:

Question 4.
In the following figures, a pair of parallel lines are cut by a transversal. Find the value of x in each figure.

Solution:

Question 5.
In the following figures (i) to (vi), a pair of parallel lines are cut by a transversal. Find the size of each lettered angle.

Solution:

Question 6.
In the given diagram, lines AB, CD and EF are parallel. Calculate the values of x and y. Hence, find the reflex angle ECA.

Solution:

Question 7.
In the given figure, l || m. Find the values of x, y and z.

Solution:

Question 8.
Calculate the measure of each lettered angle in the following figure (parallel lines, segment or rays are denoted by thick matching arrows):

Solution:

Question 9.
In the figure given below, state whether the lines l and m are parallel or not.

Solution:

ML Aggarwal Class 7 Solutions Chapter 10 Lines and Angles Ex 10.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 10 Lines and Angles Ex 10.1

Question 1.
(i) Can two right angles be complementary?
(ii) Can two right angles be supplementary?
(iii) Can two adjacent angles be complementary?
(iv) Can two adjacent angles be supplementary?
(v) Can two obtuse angles be adjacent?
(vi) Can an acute angle be adjacent to an obtuse angle?
(vii) Can two right angles form a linear pair?
Solution:

Question 2.
Find the complement of each of the following angles:

Solution:

Question 3.
Find the supplement of each of the following angles:

Solution:

Question 4.
Identify which of the following pairs of angles are complementary and which are supplementary:
(i) 55°, 125°
(ii) 34°, 56°
(iii) 137°, 43°
(iv) 112°, 68°
(v) 45°, 45°
(vi) 72°, 18°
Solution:

Question 5.
(i) Find the angle which is equal to its complement.
(ii) Find the angle which is equal to its supplement.
Solution:

Question 6.
Two complementary angles are (x + 4)° and (2x – 7)°, find the value of x.
Solution:

Question 7.
Two supplementary angles are in the ratio of 2 : 7, find the angles.
Solution:

Question 8.
Among two supplementary angles, the measure of the longer angle is 44° more than the measure of the smaller angle. Find their measures.
Solution:

Question 9.
If an angle is half of its complement, find the measure of angles.
Solution:

Question 10.
Two adjacent angles are in the ratio 5 : 3 and they together form an angle of 128°, find these angles.
Solution:

Question 11.
Find the value of x in each of the following diagrams:

Solution:

Question 12.
Find the values of x, y and z in each of the following diagrams:

Solution:

Question 13.
In the given figure, lines AB and CD intersect at F. If ∠EFA = ∠AFD and ∠CFB = 50°, find ∠EFC.

Solution:

ML Aggarwal Class 7 Solutions Chapter 9 Linear Equations and Inequalities Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 9 Linear Equations and Inequalities Check Your Progress

Question 1.
Solve the following equations :
(i) 2 (x – 5) + 3 (x – 2) = 8 + 7 (x – 4)

Solution:

Question 2.
A number exceeds its three-fifth by 22. Find the number.
Solution:

Question 3.
When 9 is added to twice a number, the result is 3 more than thrice the number. Find the number.
Solution:

Question 4.
The ten’s digit of a two digit number is twice the unit’s digit. The sum of the number and its unit’s digit is 66. Find the number.
Solution:

Question 5.
A student bought some pens at ₹ 8 each and some pencils at ₹ 1.50 each. If the total number of pens and pencils purchased is 16 and their total cost is ₹ 50, how many pens did he buy?
Solution:

Question 6.
Arvind is eight years older than his sister. In three years, he will be twice as old as his sister. How old are they now?
Solution:

Question 7.
The angles of a triangle are in the ratio 1 : 2 : 3. Find their measure in degrees.
Solution:

Question 8.
Solve the following inequations and represent their solution on a number line:

Solution: