The interior angles of a polygon are 3x^{}, 2x^{}, 4x^{}, 3x^{} and 6x^{}. Find the size of the smallest angle of the polygon.

Correct Answer is : 60∘^{}∘

Correct Answer is : 60∘^{}∘

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WAEC Mathematics 2019 Paper

Question : 32

Total: 50

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. Find the size of the smallest angle of the polygon.

Solution:

Concept:

The sum of the interior angles of a polygon with

n

sides is

(n-2) \times 180^\circ

Explanation:

The given angles are

3x^\circ

2x^\circ

4x^\circ

3x^\circ

, and

6x^\circ

Since there are 5 angles, the polygon is a pentagon.

So, the sum of the interior angles is

(5-2) \times 180^\circ = 540^\circ

Therefore,

3x^\circ + 2x^\circ + 4x^\circ + 3x^\circ + 6x^\circ = 540^\circ

This gives

18x^\circ = 540^\circ

Dividing both sides by 18,

x = 30

The smallest angle is

2x^\circ = 2 \times 30^\circ = 60^\circ

Answer:

The size of the smallest angle is

60^\circ

, which is option B.

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