Question

In a regular ploygon, each interior angle is thrice the exterior angle. The number of sides of the polygon is

Answer 1

★Given:-

• In a regular polygon, each interior angle is thrice the exterior angle.

★To find:-

• The number of sides of the polygon.

★Solution:-

Let the exterior angle is x.

Given that each interior angle is thrice exterior angle.

Therefore, interior angle = 3x

We know,

✦The sum of the interior and exterior angles must be 180°

Therefore,

➜x + 3x = 180

➜4x = 180

➜x = 180/4

➜x = 45

Interior angle = 3x

➜3(45)

➜135°

Exterior angle = x = 45°

✦The exterior angles of a regular polygon add up to 360.

Using the formula,

✦n × each exterior angle = 360

Where,

➜n=number of sides

Putting values,

➜360/n = 45

➜n = 360/45

➜n = 8

Therefore,the number of sides of the polygon is 8.

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