In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80º. Find ∠QRS.
Attached Figure / Diagram
A
90o
B
80o
C
50o
D
40o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
QOP = 180 - 100(straight line angle) → 80^\circ
OPQ and OQP are isosceles of 40^\circ each.
∠QRS = ∠RPQ (theorem: angle in the alternate segment are equal)
∠RPQ = 40º
∠QRS = 40º
Source: WAEC / JAMB / NECO Classroom Archive (Record #26645)