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JAMB Mathematics 2014 Paper

Question : 23

Total: 47

How many sides has a regular polygon whose interior angle is 135°?

Solution:

Concept:

For a regular polygon, each exterior angle is the supplement of each interior angle.

Explanation:

The interior angle is

135^\circ

So, each exterior angle is

180^\circ - 135^\circ = 45^\circ.

The sum of all exterior angles of any polygon is

360^\circ

For a regular polygon, the number of sides is given by

\text{Number of sides} = \frac{360^\circ}{\text{one exterior angle}}.

Therefore,

\frac{360^\circ}{45^\circ} = 8.

Answer:

The polygon has

8

sides.

Correct option: D.

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