In a regular polygon each interior is thrice the exterior angle then number sides have?

Given:  In a regular polygon each interior is thrice the exterior angle

To do: Find the number of sides.

Solution:

Let the Exterior angle be 'a'

Interior angle = 3a

We know that,

Exterior angle $+$ Interior angle = 180

=> $a + 3a = 180$

=> $4a = 180$

=> $a = 45°$

Interior angle = $3 \times 45 = 135°$

Exterior angle = 45°

Let us say the polygon has n sides

Sum of the n exterior angles = 360

$=> n \times 45 = 360$

=> $n = 8$

Therefore there are 8 sides

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Updated on: 10-Oct-2022

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