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WAEC Mathematics 2011 Paper

Question : 8

Total: 47

A regular polygon of n sides has each exterior angle to 45^o. Find the value of n

Solution:

Concept:

For any regular polygon, the sum of all exterior angles is

360^\circ

. Since all exterior angles are equal, each exterior angle is

\frac{360^\circ}{n}

Explanation:

Each exterior angle of a regular polygon with

n

sides is given by:

\text{Exterior angle} = \frac{360^\circ}{n}

Given that each exterior angle is

45^\circ

, we set up the equation:

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

Multiply both sides by

n

45^\circ n = 360^\circ

Divide both sides by

45^\circ

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

Answer:

n = 8

Correct option: B. 8

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