You can Download KSEEB Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Questions and Answers helps you to revise the complete syllabus.

## KSEEB Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

Question 1.

Find x in the following figures:

Solution:

∠XNE + ∠ENT = 180° (Linear pair)

⇒ 125° + ∠ENT = 180°

⇒ ∠ENT = 180° – 125°

∴ ∠ENT = 55°

Similarly, ∠NET = 55°

In ∆NET,

∠N + ∠E + ∠T = 180°

⇒ 55° + 55° + ∠T = 180°

⇒ 110° + ∠T = 180°

⇒ ∠T = 180° – 110°

∴ ∠T = 70°

∠NTE + ∠x° = 180°

⇒ 70° + ∠x = 180°

⇒ ∠x = 180° – 70°

∴ ∠x = 110°

(b) ∠DCQ + ∠DCB = 180° (Linear pair)

⇒ 60° + ∠DCB = 180°

⇒ ∠DCB = 180° – 60°

∴ ∠DCB = 120°

∠AES + ∠AED = 180° (Linear pair)

⇒ 70° + ∠AED = 180°

⇒ ∠AED = 180° – 70°

∴ ∠AED = 110°

∠RDE + ∠EDC = 180° (Linear pair)

⇒ 90° + ∠EDC = 180°

⇒ ∠EDC = 180° – 90°

∴ ∠EDC = 90°

∠ABC + ∠CBP = 180° (Linear pair)

⇒ 90° + ∠CBP = 180°

⇒ ∠CBP = 180° – 90°

∴ ∠CBP = 90°

∠SEA + ∠TAB + ∠CBP + ∠DCQ + ∠RDE = 360° (Sum of exterior angles of a polygon)

⇒ 70° + x + 90° + 60° + 90° = 360°

⇒ 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) Sum of exterior angles = 360°

No. of sides = 9

∴ Measure of each exterior angle = \(\frac{360^{\circ}}{9}\) = 40°

(ii) Sum of exterior angles = 360°

No. of sides = 15

∴ Measure of each exterior angle = \(\frac{360^{\circ}}{15}\) = 24°

Question 3.

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

Solution:

Sum of measures of exterior angles of a polygon = 360°

Measure of exterior angle = 24°

∴ No. of sides = \(\frac{360^{\circ}}{24}\) = 15

Hence, No. of sides of a polygon = 15

Question 4.

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

Solution:

Each interior angle = 165°

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

Sum of measure of exterior angles = 360°

No. of sides = \(\frac{360^{\circ}}{15}\) = 24

Hence, 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?

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

Solution:

(a) Equilateral triangle is a regular polygon of 3 sides.

So, each interior angle = \(\frac{180^{\circ}}{3}\) = 60°

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