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]

Answers

  1. Step-by-step 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.

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