Question

The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides. 20

Answer 1

Answer:

Internal angle = $160^\circ$

Number of sides = 18

Step-by-step explanation:

Given that:

We have a regular polygon with number of sides unknown.

Measure of an exterior angle of the polygon = $20^\circ$

To find:

Measure of an interior angle and the number of sides of the polygon?

Solution:

Let us have a look at the relation of sum of external angles.

Sum of one internal angle and its corresponding external angle = $180^\circ$

Internal angle + external angle = $180^\circ$

Internal angle = $180^\circ$ - $20^\circ$ = $160^\circ$

Sum of all the external of a regular polygon = $360^\circ$

All the external angles will be equal because it is a regular polygon.

Let the number of sides = $n$

Therefore,

$n \times 20^\circ = 360^\circ\\\Rightarrow n = 18$

Therefore, the answers are:

Internal angle = $160^\circ$

Number of sides = 18