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WAEC Mathematics 2023 Paper

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Question : 39

Total: 50

In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.

$42^{0}$
$35^{0}$
$20^{0}$
$90^{0}$

Solution:

Concept:

An angle in a semicircle is

90^\circ

, and the exterior angle of a triangle equals the sum of the two opposite interior angles.

Explanation:

Since

NR

is a diameter,

\angle RMN = 90^\circ

.

In

\triangle RMN

,

\angle SRN

is the exterior angle.

Thus,

\angle SRN = \angle RMN + \angle MNR

.

Substituting gives

5x + 20 = 90 + x

.

So,

5x - x = 90 - 20

.

Therefore,

4x = 70

.

x = \frac{70}{4} = 17.5^\circ

.

Hence,

2x = 2 \times 17.5 = 35^\circ

.

Answer:

2x = 35^\circ

Option B.

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