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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:

∠RMN = 90° (angles in a semicircle is a right angle)

∠SRN = ∠RMN + ∠MNR (ext. angle of a ∆ is equal to the sum of two opp. int. angles)

⇒ 5x + 20 = 90 + x

⇒ 5x - x = 90 - 20

⇒ 4x = 70

x = $\;\frac{70}{4}$

= 17.4°

therefore, 2x = 2 $\times 17.5$ = 35°

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