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BECE Mathematics 2010 Paper

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Question : 29

Total: 40

The interior angle of a regular polygon is

120^{\circ}

. How many sides has the polygon?

3
4
5
6

Solution:

Concept:

For a regular polygon with

n

sides, each interior angle is given by

\frac{(n-2) \times 180^\circ}{n}

.

Explanation:

Let the number of sides be

n

.

The interior angle is

120^\circ

.

So,

\frac{(n-2) \times 180}{n} = 120

.

Multiply both sides by

n

:

(n-2) \times 180 = 120n

.

Expand the left side:

180n - 360 = 120n

.

Subtract

120n

from both sides:

180n - 120n = 360

.

Simplify:

60n = 360

.

Divide both sides by

60

:

n = \frac{360}{60} = 6

.

Answer:

The polygon has

6

sides.

Correct option: D.

6

.

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