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JAMB Mathematics 2012 Paper

Question : 23

Total: 48

Solution:

Concept:

There are 5 angles, so the polygon is a pentagon.

Use the sum of interior angles of a pentagon to solve for

x

Explanation:

The sum of the interior angles of a polygon is

(n - 2) \times 180^\circ

For a pentagon,

n = 5

So, sum of interior angles

= (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ

The given angles are

x

2x

3x

4x

, and

5x

Their sum is

x + 2x + 3x + 4x + 5x = 15x

Thus,

15x = 540^\circ

x = \frac{540^\circ}{15} = 36^\circ

Answer:

x = 36^\circ

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