In the diagram above, if ∠RPS = 50o, ∠RPQ = 30o and PQ = QR, find the value of ∠PRS.
Attached Figure / Diagram
A
80o
B
70o
C
60o
D
50o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\Delta PQR is isosceles
∴∠PRQ = 30o
Also in \Delta PQR
^Q = 180 -(30 + 30)
= 120o
PQRS is a cyclic quad
∴^S + ^Q = 180(opp ∠s of a cyclic quad)
S + 120 = 180
S = 60o
In \DeltaPSR
x + 50 + 60
= 180(sum of ∠s of a \Delta)
x + 110 = 180
x = 180 - 110
x = 70o
Source: WAEC / JAMB / NECO Classroom Archive (Record #10411)