Haryana State Board HBSE 8th Class Maths Solutions Chapter 3 Understanding Quadrilaterals Ex 3.2 Textbook Exercise Questions and Answers.

## Haryana Board 8th Class Maths Solutions Chapter 3 Understanding Quadrilaterals Exercise 3.2

Question 1.

Find x in the following figures :

Solution:

(a)

∠XAB + ∠BAC = 180°

or 125° + ∠BAC = 180°

∠BAC = 180° – 125° = 55

∴ ∠BAC = 55°

∠ABC + ∠QBC = 180°

∠ABC + 125° = 180°

∴ ∠ABC = 180° – 125° = 55°

In △ABC.∠A + ∠B + ∠C = 180°

55° + 55° + ∠C = 180°

110°+ ∠C = 180°

∴ ∠C = 180°-110° = 70°

∠ACB + ∠x = 180° [Linear pair]

70° + ∠x = 180°

∴ ∠x = 180°-70° = 110°

2nd Method : Sum of the measures of the external angles of any polygon is 360°.

∴ 125° + 125° + x = 360°

or 250° + x = 360°

∴ x = 360° – 250° = 110°

(b) ∠DCQ + ∠DCB = 180°

or 60° + ∠DCB = 180°

∴ ∠DCB = 180° – 60° = 120°

∠AES + ∠AED = 180°

70° + ∠AED = 180°

∠AED = 180° – 70° = 110°

∠RDE + ∠EDC = 180°

90° + ∠EDC = 180°

∴ ∠EDC = 90°

∠ABC + ∠CBP = 180°

90° + ∠CBP = 180°

∴ ∠CBP = 90°

∠SEA + ∠TAB + ∠CBP + ∠DCQ + ∠RDE = 360°

70° + x + 90° + 60° + 90° = 360°

or x + 310° = 360°

∴ ∠x = 360°-310°

∴ ∠x = 50°.

Question 2.

Find the measure of each exterior angle of a regular polygon of

(i) 9 sides

(ii) 15 sides.

Solution:

(i)Total measure of all exterior angles = 360°

Total number of sides = 9

Therefore, the measure of each exterior angle = \(\frac{360}{9}\) = 40°

(ii) Total measure of all exterior angle = 360°

Total number of sides = 15

Therefore, the measure of each exterior angle = \(\frac{360}{15}\) = 24°

Question 3.

How many sides does a regular polygon have if the measure of an exterior angle is 24° ?

Solution:

Total measure of all exterior angle = 360°.

The measure of an exterior angle is 24.

Therefore, the number of sides = \(\frac{360}{24}\) = 15.

∴ The number of sides = 15.

Question 4.

How many sides does a regular polygon have if each of its interior angles is 165°?

Solution:

Each interior angle of a polygon = 165°

∴ Each exterior angle = 180° – 165° = 15°

Sum of exterior angles = 360°

∴ Number of sides = \(\frac{360}{15}\) = 24

∴ Polygon has 24 sides.

Question 5.

(a) Is it possible to have a regular polygon with measure of each exterior angle as 22° ?

(b) Can it be an interior angle of a regular polygon ? Why ?

Solution:

(a) No; (since 22 is not a divisor of 360).

(b) No; because each exterior angle is 180° – 22° = 158°, which is not a divisor of 360°.

Question 6.

(a) What is the minimum interior angle possible for a regular polygon ? Why?

(6) What is the maximum exterior angle possible for a regular polygon?

Solution:

(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle = 60°.

(b) By (a), we can see that the greatest exterior angle = (180° – 60°) = 120°.