Question

a) The ratio between an exterior angle and interior angle of a regular polygon is 1: 5. Find (i) measure of each exterior angle (ii) measure of each interior angle
(iii) The number of sides in the polygon

Answer 1

Answer:

The ratio between the exterior angle and interior angle of a regular polygon is 2:3.

Each interior angle of a regular polygon =

n

180

o

(n−2)

where n = number of sides of polygon

Each exterior angle of a regular polygon =

n

360

o

According to question,

n

360

o

:

n

180

o

(n−2)

=2:3

=>

(n−2)

2

=

3

2

=>n−2=3

=>n=5