Question

find the number of sides of a regular polygon if each of its interior angle is 108

Answer 1

Answer:

The polygon has 5 sides

Step-by-step explanation:

For a regular polygon with n sides,

Sum of interior angles = 180 ( n - 2 ).

Thus, measure of each interior angle:

[ 180 ( n - 2 ) ] / n

Thus,

108 = [ 180 ( n - 2 ) ] / n

108 n = 180 n - 360

72 n = 360

n = 5

Answer 2

Given :

Interior angle of a regular polygon is 108 degree.

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To find :

Find the number of sides of a regular polygon.

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Using formula :

★ Number of sides = 360/Exterior angle.

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We know that :

Exterior angle is not know to us so, let's find the exterior angle to find apply the above formula in the calculations.

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Finding the exterior angle :

→ Exterior angle = 180° - 108°

→ Exterior angle = 72°

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Calculations :

→ Number of sides = 360/72

→ Number of sides = 5

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Therefore, number of sides of the polygon is 5 sides.