Find the measure of an are exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?

Solution:

We have to find the measure of the exterior angle of a regular pentagon and a regular decagon.

We know, the exterior angle of a regular polygon = 360°/n,

Where n is the number of sides of a polygon.

For a regular pentagon, n = 5

Exterior angle = 360°/5 = 72°

For a regular decagon, n = 10

Exterior angle = 360°/10 = 36°

We have to find the ratio of these two angles.

Required ratio = 72° : 36°

= 2 : 1

Therefore, the required ratio is 2:1.

✦ Try This: Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular hexagon. What is the ratio between these two angles?

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 168

Find the measure of an are exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?

Summary:

The measure of an exterior angle of a regular pentagon and an exterior angle of a regular decagon are 72° and 36°. The ratio between these two angles is 2 : 1.

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