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The ratio between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.

Solution:

Given, the ratio between exterior angle and interior angle of a regular polygon is 1 : 5.

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

Let the interior angle be 5x and the exterior angle be x.

We know, exterior angle = 180° - interior angle.

x = 180° - 5x

Now, x + 5x = 180°

6x = 180°

x = 180°/6

x = 30°

Therefore, the measure of each exterior angle is 30°.

Now, number of sides of a polygon = 360°/measure of exterior angle

= 360°/30°

= 36/3

= 12

Therefore, the number of sides is 12.

✦ Try This: The ratio between exterior angle and interior angle of a regular polygon is 1:6. Find the number of sides of the polygon.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 140

Summary:

The ratio between exterior angle and interior angle of a regular polygon is 1:5. The number of sides of the polygon is 12.

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