Question

1. A regular polygon has an interior angle of 144˚, workout. [4]

(a) The exterior angle

(b) The number of sides​

Answer 1

ⓢⓞⓛⓤⓣⓘⓞⓝ

Required data,

each interior angle of a regular polygon=144°

To solve the sum we use the formula of exterior angle and formula of number of sides

1.a)

we know that sum of each Interior angle and exterior angle is 180° of a regular polygon

here interior angle=144°

therefore exterior angle=180°-144°=36°

b) number of sides =360°/each exterior angle

=360°/36°

=10

Regular polygon is a type of polygon who has equal sides and equal angles

Diagonal of a regular polygon=n(n-3)/2

so here number of diagonal=10(10-3)/2=10×7/2=5×7=35 diagonals