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WAEC Physics 2015 Paper

Question : 50

Total: 50

Solution:

Concept:

The sum of the interior angles of a pentagon is

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

Explanation:

Let the two angles in the ratio

2:3

2x

and

3x

The other three angles are each

60^\circ

, so their sum is

3 \times 60^\circ = 180^\circ

Write the total angle sum equation:

2x + 3x + 180^\circ = 540^\circ

This simplifies to

5x + 180^\circ = 540^\circ

Subtract

180^\circ

from both sides:

5x = 360^\circ

Divide by

5

x = \frac{360^\circ}{5} = 72^\circ

Thus, the two angles are:

2x = 2 \times 72^\circ = 144^\circ

and

3x = 3 \times 72^\circ = 216^\circ

The smaller of these two angles is therefore

144^\circ

Answer:

144^\circ

(Option D).

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