In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x +...
MATHEMATICS
WAEC 2023
In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.
- A. \(42^0\)
- B. \(35^0\)
- C. \(20^0\)
- D. \(90^0\)
Correct Answer: B. \(35^0\)
Explanation
∠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\(\times17.5\) = 35°
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