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 is B
∠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°