Question

Find the measures of an interior angle and an exterior angle of a regular 20-gon

Answer 1

Given:

20-sided polygon

To find:

The interior and the exterior angle

Solution:

The required interior angle is 162° and the exterior angle is 18°.

We can obtain the required measures by using the given polygon's sides.

We know that the polygon's exterior angle=360°/ number of sides

Using the values,

=360°/20

=18°

Now, the sum of the polygon's interior and exterior angle is 180°.

So, interior angle+exterior angle=180°

Interior angle+18°=180°

Interior angle=180°-18°

=162°

Therefore, the required interior angle is 162° and the exterior angle is 18°.