Question

(2)
U
10. In a regular polygon, each interior angle is thrice the exterior angle. The number of sides of
the polygon is
(a) 6
(d) 12
sides of
A
8
(c)
10​

Answer 1

Answer:

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

the polygon is 8

Step-by-step explanation:

Let n be the number of sides of the regular polygon.

The sum of the interior angles of a regular polygon is given by:

Sum = (n - 2)180

Therefore, one interior angle = [(n - 2)180] / n

The sum of exterior angles of a polygon is equal to 360°

So, one exterior angle equals to = 360/n

From the question, each interior angle is thrice the exterior angle.

So, we have:

[(n - 2)180]/n = 3 (360/n)

[(n - 2)180]/n = 1080/n

Multiply both sides by n to get:

n[(n - 2)180) = 1080 n

180n² - 360n = 1080n

180n² = 1080n + 360n

180n² = 1440n

n = 1440n/180n

n = 8

The number of sides of the regular polygon is 8.