Question

A regular polygon of n sides is such that each interior angle is 120° greater than the exterior angle. Find

(i) the value of n
(ii) the sum of all the interior angles​

Answer 1

n = 12 , sum = 1800°

Explanation:

let e represent an exterior angle then interior angle is e + 120

(i)

in any polygon

exterior angle + interior angle = 180° , then summing the 2 angles

e + e + 120 = 180

2e + 120 = 180 ( subtract 120 from both sides )

2e = 60 ( divide both sides by 2 )

e = 30

Thus exterior angle = 30°

the sum of the exterior angles in a polygon = 360°

since the polygon is regular then each interior angle is 30° , then

n = 360° ÷ 30÷ = 12

(ii)

the sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

here n = 12 , so

sum = 180° × (12 - 2) = 180° × 10 = 1800°