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The ratio of exterior angle to interior angle of a regular polygon is 1:4. Find the number of sides of the polygon.

Solution:

Given, the ratio of exterior angle to interior angle of a regular polygon is 1 : 4

We have to find the number of sides of the polygon.

Let the exterior angle of a polygon be x.

Interior angle = 180° - exterior angle

So, interior angle = 180° - x

According to the question,

x/(180° - x) = 1/4

On cross multiplication,

4x = 180° - x

By transposing,

4x + x = 180°

5x = 180°

x = 180°/5

x = 36°

Number of sides of a polygon = 360°/exterior angle

= 360°/36°

= 10

Therefore, the number of sides of a polygon is 10.

✦ Try This: The ratio of exterior angle to interior angle of a regular polygon is 2 : 5. Find the number of sides of the polygon.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 32

Summary:

The ratio of exterior angle to interior angle of a regular polygon is 1:4. The number of sides of the polygon is 10.

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