Question

To the nearest degree, what is the measure of each exterior angle of a regular decagon?

Answer 1

Answer:

Exterior angle of a decagon will be 36°

Step-by-step explanation:

Measure of all interior angles of a polygon is represented by (n - 2)×180°

where n is the number of sides of the polygon.

Now we have to calculate the exterior angle of a regular decagon.

As we know exterior angle of polygon is supplementary of the interior angle.

So we will calculate interior angle first.

Sum of interior angles of decagon = (n - 2)×180° = 8×180° = 1440°

Since decagon is regular so all angles will be same.

So one angle of decagon = 1440 ÷ 10 = 144°

Now exterior angle = 180 - 144 = 36°

Each exterior angle of a decagon will be 36°.