Question

2. Find the number of sides in a regular polygon,
if its each interior angle is :
(i) 160°
(ii) 135
1
(iii) 1 1/5 of a right angle​

Answer 1

Answer:

(i) Let no. of sides of regular polygon be n.

Each interior angle = 160°

∴ (n – 2)/n × 180° = 160°

180n – 360° = 160n

180n – 160n = 360°

20n = 360°

n = 18

(ii) No. of sides = n

Each interior angle = 135°

(n – 2)/n × 180° = 135°

180n – 360° = 135°

180n – 135n = 360°

45n = 360°

n = 8

(iii) No. of sides = n

Each interior angle = 1.1/5 right angles

= 6/5 × 90

= 108°

∴ (n – 2)/n × 180° = 108°

180n – 360° = 108n

180n – 108n = 360°

72n = 360°

n = 5