Question

The diagram shows part of a regular polygon.

The exterior angle is xº.
The interior angle is 29xº.
Work out the number of sides of this polygon.
29xº
to
NOT TO
SCALE
[3]

Answer 1

Explanation:

the sum of all external angles in a polygon is 360°.

a single external angle is therefore 360/n °.

the sum of all internal angles is

(n - 2) × 180

a single internal angle is then

(n-2) × 180 / n

with n being the number of sides.

the internal and the external angle are together 180°.

so, we know

x + 29x = 180

30x = 180

x = 6°

360/n = x

360/x = n

360/6 = 60

so, this polygon has 60 sides.