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JAMB Mathematics 2015 Paper

Question : 56

Total: 61

How many sides has a regular polygon whose interior angles are 120°each

Solution:

Concept:

For any regular polygon, each exterior angle is

180^\circ - \text{interior angle}

, and the sum of exterior angles is

360^\circ

Explanation:

The interior angle is

120^\circ

So each exterior angle is

180^\circ - 120^\circ = 60^\circ

Let

n

be the number of sides.

The exterior angle of a regular polygon is given by

\frac{360^\circ}{n}

Therefore,

60^\circ = \frac{360^\circ}{n}

Solving for

n

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

Answer:

The polygon has

6

sides, so the correct option is C.

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