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Example 10: Find the number of sides of a regular polygon if the exterior angle is one-fourth of
its interior angle.

Solution: Let the number of sides of a regular polygon be n.
According to question,
1
Exterior angle = × interior angle
4
360° 1 (n − 2 ×) 180°
fi = ×
n 4 n Think and Answer
fi 360° × 4 = (n – 2) × 180° Is it possible to have a regular
fi 8 = n – 2 polygon with a measure of
each exterior angle as 22°?
\ n = 10
Thus, the number of sides of the regular polygon is 10.

Practice Time 3B

C 80° B
1. Find the value of ‘x’ in the given figure ABCD. 70°

2. Find the measure of an exterior angle of a regular polygon of 12 sides.
70°
3. Find the number of sides of a regular polygon whose each exterior angle is 90°. A
4. What is the maximum exterior angle possible for a regular polygon? Why? D x
5. Each interior angle of a regular polygon is 140°. Find the number of its sides.
6. Find the value of ‘x’ in the given polygon.
(a) E (b) A
90°
60° 30°
A 90° D
B 40° D x
∠1
C x
B 40° 45°
C
7. Find the value of

(a) x + y + z (b) x + y + z + w

z
60°
x
90° y
z 30° w 120° 80° z
y x p a a
8. Observe the adjoining figure, and answer the following questions. y
a a
(a) What is the sum of the measures of exterior angles x, y, z, p, q, r? q
(b) Is x = y = z = p = q = r? Why? a a x
(c) What is the measure of each: (i) exterior angle? (ii) interior angle? r

9. Find the ratio of interior and exterior angle of a regular octagon.
10. Find the number of sides of a regular polygon if the exterior angle is one-fifth of its interior angle.

63 Quadrilaterals