In the given figure, PQ = PS = SR and ∠QPS = 40o, then what is the value of ∠QPR (in degrees)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 75°.
In △PQS:
PS = PQ
∠QSP = ∠PQS
θ + θ + 40° = 180°
⇒ θ = 70° = ∠QSP
⇒ ∠PSR = 180° - 70° = 110°
In △PSR:
PS = RS
∠PRS = ∠SPR = α (let)
⇒ 2α + 110 = 180°
⇒ α = 70°/2 = 35°
Hence,
∠QPR = 40° + 35° = 75°