## RS Aggarwal Class 7 Solutions Chapter 15 Properties of Triangles Ex 15A

These Solutions are part of RS Aggarwal Solutions Class 7. Here we have given RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15A.

**Other Exercises**

- RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15A
- RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15B
- RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15C
- RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15D

**Question 1.**

**Solution:**

In ∆ABC,

∠A = 72°, ∠B = 63°

But ∠A + ∠B + ∠C = 180° (Sum of angles of a triangle)

⇒ 72° + 63° + ∠C = 180°

⇒ 135° + ∠C = 180°

⇒ ∠C= 180°- 135° = 45°

**Question 2.**

**Solution:**

In. ∆PQR,

∠E = 105°, and ∠F = 40°

But ∠D + ∠E+ ∠F= 180° (sum of angles of a triangle)

⇒ ∠D + 105°+ 40°= 180°

⇒ ∠ D + 145° = 180°

⇒ ∠D = 180°- 145°

⇒ ∠D = 35°

**Question 3.**

**Solution:**

In ∆XYZ,

∠ X = 90°, ∠ Z = 48°

But ∠X + ∠Y + ∠Z = 180° (Sum of angles of a triangle)

⇒ 90° + ∠ Y + 48° = 180°

⇒ 138°+ ∠ Y = 180°

⇒ ∠Y = 180° – 138° = 42°

⇒ ∠Y = 42°

**Question 4.**

**Solution:**

Sum of angles of a triangle = 180°

and ratio in the three angles = 4 : 3 : 2

**Question 5.**

**Solution:**

In a right triangle

Sum of the two acute angles = 90°

One angle = 30°

Second angle = 90° – 36° = 54°

**Question 6.**

**Solution:**

In a right triangle

Sum of two acute angles = 90°

and ratio of these two angles = 2 : 1

Let first angle = 2x

Then second angle = x

2x + x = 90°

⇒ 3x = 90°

⇒ x = \(\frac { 90 }{ 3 }\) = 30°

First angle = 2x = 2 x 30° = 60°

and second angle = x = 1 x 30° = 30°

**Question 7.**

**Solution:**

In a triangle,

Measure of one angle = 100°

Sum of other two angles = 180° – 100° = 80°

(Sum of angles of a triangles)

But, these two angles are equal.

Measure of each angle = \(\frac { 80 }{ 2 }\) = 40°

**Question 8.**

**Solution:**

Sum of angles of a triangle = 180°

Let third angle = x

then, each equal angles = 2x

x + 2x + 2x = 180°

⇒ 5x = 180°

⇒ x = \(\frac { 180 }{ 5 }\) = 36°

Each equal angle = 2x = 2 x 36° = 72°

and third angle = 36°

**Question 9.**

**Solution:**

In a triangle ABC,

Let ∠A = ∠B + ∠C

But ∠A + ∠B + ∠C = 180° (Sum of angles of a triangle)

⇒ ∠A + ∠A = 180° (∠B + ∠C = ∠A)

⇒ 2A = 180°

⇒ ∠ A = \(\frac { 180 }{ 2 }\) = 90°

∠ A = 90°

Hence, ∆ABC is a right triangle.

**Question 10.**

**Solution:**

In a ∆ABC,

2 ∠A = 3 ∠B = 6 ∠C = 1 (suppose)

**Question 11.**

**Solution:**

In an equilateral triangle,

All sides are equal.

All angles are also equal.

Each angle = \(\frac { 180 }{ 3 }\) = 60°

(Sum of angles of a triangle = 180°)

**Question 12.
**

**Solution:**

In the given figure,

ABC is a triangle in which DE || BC,

∠A = 65° and ∠B = 55°

DE || BC and ADB is the transversal

⇒ ∠ ADE = ∠ B (corresponding angles) = 55° (∠B = 55°)

In ∆ADE,

∠A + ∠ADE + ∠AED = 180° (sum of angles of a triangle)

⇒ 65° + 55° + ∠AED = 180°

⇒ ∠ 120° + ∠AED = 180°

⇒ ∠AED = 180°- 120° = 60°

∠AED = 60°

D || BC and AEC is the transversal

∠ C = ∠ AED (A corresponding angles)

∠C = 60°

Hence ∠ADE = 55°, ∠AED = 60° and ∠ C = 60°

**Question 13.**

**Solution:**

(i) No. In a triangle, only one right angle is possible as if there are two right angles, then The third angle will be ∠ero which is not possible.

(ii) No. In a triangle only one obtuse angle is possible as if there are two obtuse angles, then the sum of these two angles will be greater than 180° which is not possible.

(iii) Yes. two acute can arc possible.

(iv) No. The sum of these three angles will be greater than 180° which is not possible in a triangle.

(v) No. The sum of these angles will be less than 180° which is not possible.

(vi) Yes. The sum of there three angle will be in 180° which is possible.

**Question 14.**

**Solution:**

(i) Yes, it can be a right triangle also

(ii) Yes, if right triangle has its sides different then it is possible.

(iii) No, a right triangle cannot be an equilateral triangle as an equilateral triangle has each side 60°.

(iv) Yes, it is possible, if its sides opposite to acute angles are equal.

**Question 15.**

**Solution:**

(i) A right triangle cannot have an obtuse angle.

(ii) The acute angles of a right triangle are complementary.

(iii) Each acute angle of an isosceles right triangle measures 45°.

(iv) Each angle of an equilateral triangle measures 60°.

(v) The side opposite the right angle of the right triangle is called the hypotenuse.

(vi) The sum of the lengths of the sides of a triangle is called its perimeter.

Hope given RS Aggarwal Solutions Class 7 Chapter 15 Properties of Triangles Ex 15A are helpful to complete your math homework.

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