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JAMB Mathematics 2023 Paper

Question : 6

Total: 80

Solution:

Concept:

For any regular polygon, the number of sides

n

can be found by comparing its interior and exterior angles.

Explanation:

Let the number of sides be

n

Interior angle of a regular polygon =

\frac{(2n-4)\times 90}{n}

Exterior angle of a regular polygon =

\frac{360}{n}

Given that interior angle =

5 \times

exterior angle:

\frac{(2n-4)\times 90}{n} = 5 \times \frac{360}{n}

Multiply both sides by

n

(2n-4)\times 90 = 5 \times 360

180n - 360 = 1800

180n = 2160

n = \frac{2160}{180} = 12

A polygon with 12 sides is a dodecagon.

Answer:

A. dodecagon

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