Question

Each interior angle of a regular polygon measures 156. How many sides does the polygon have?

Answer 1

Answer:

Step-by-step explanation:

) Let the polygon be n-sided.

Given that Each interior angle measures 156°

So, ( n-2 ) × 180 / n = 156

=> 180n - 360 = 156n .

=> 180n - 156n = 360

=> 24 n = 360

=> n = 360/24 = 180/12 = 90/6 = 15 .

=> n = 15 sides.

Therefore ,The polygon with each interior angle 156° has 15 sides.

2) Let the polygon be n-sided.

Given that Each interior angle measures 108°

So, ( n-2 ) × 180 / n = 108°

=> 180n - 360 = 108n .

=> 180n - 108n = 360

=> 72 n = 360

=> n = 360/72= 5

=> n = 5 sides.

Therefore ,The polygon with each interior angle 108° has 5 sides.