Question

Find the number of sides in a regular
polygon, its interior angle is equal to its
exterior angle​

Answer 1

Step-by-step explanation:

The sum of exterior angle and its adjacent interior is 180

0

, that is,

e+i=180

0

Since each exterior angle is equal to one third its adjacent interior angle, therefore, substitute

3

i

=e or i=3e.

e+3e=180

0

⇒4e=180

0

⇒e=

4

180

0

=45

0

We know that the measure of exterior angle is e=(

n

360

)

0

where n is the number of sides.

Here, it is given that the exterior angle is e=45

0

, therefore,

n=

e

360

=

45

360

=8

Hence, the number of sides is 8.