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BECE Mathematics 2016 Paper

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Question : 30

Total: 40

The sum of the interior angles of a regular polygon is

540^{\circ}

. Find the number of sides of the polygon.

7
6
5
4

Solution:

Concept:

The sum of the interior angles of an

n

-sided polygon is given by

(n-2)\times 180^\circ

.

Explanation:

Let

n

be the number of sides of the regular polygon.

The given sum of interior angles is

540^\circ

.

Using the formula:

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

.

Divide both sides by

180^\circ

to get:

n-2 = \frac{540^\circ}{180^\circ} = 3

.

Add

2

to both sides:

n = 3+2 = 5

.

So, the regular polygon has 5 sides.

Answer:

C. 5

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