In the diagram, NR is a diameter, ∠MNR = x° and, ∠SRN = (5x + 20)°. Find the value of 2x.
Attached Figure / Diagram
A
\(42^0\)
B
\(35^0\)
C
\(20^0\)
D
\(90^0\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
∠RMN = 90^\circ (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^\circ
therefore, 2x = 2\(\times17.5\) = 35^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #69167)