The interior angle of a regular polygon is five times its corresponding exterior angle. Find the

number of sides of the polygon.

1405

B - -+

e

w

hp

%

8

$

5

6

12

Step-by-step explanation:

Regular polygon is one in which each angle and sides is congruent.

Sum of all the exterior angles of any polygon is 360.

Sum of all the interior angles of any polygon is (2n-4) * 90

where is n is the no. of sides of polygon.

Let n be the no. of sides of polygon required

Therefore,

Sum of all the interior angles of polygon = (2n-4) * 90

since no of sides of polygon is n

therefore, value of each interior angles of the polygon = (2n-4) * 90/n (A)

Sum of all the exterior angles of any polygon = 360.

value of each exterior angles of the polygon = 360/n (B)

Given that

The interior angle of a regular polygon is five times its corresponding exterior angle (c)

using the statement A, B and C

(2n-4) * 90/n = 5*360/n

1/n is common on both side, hence it gets cancelled.

(2n-4) * 90 = 5*360

=> (2n-4) = 5*360 / 90 = 20

=> 2n = 20+4 = 24

=> n = 24/2 = 12.

the number of sides of the polygon is 12