In the diagram above, if ∠ RPS = 50o, ∠ RPQ = 30o and PQ = QR, find the value of ∠ PRS.
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Correct Answer: Option B
Explanation:
Δ PQR is isosceles
−∠ PRQ = 30o
Also in Δ 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 ΔPSR
x + 50 + 60
= 180(sum of ∠ s of a Δ)
x + 110 = 180
x = 180 - 110
x = 70o
Δ PQR is isosceles
−∠ PRQ = 30o
Also in Δ 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 ΔPSR
x + 50 + 60
= 180(sum of ∠ s of a Δ)
x + 110 = 180
x = 180 - 110
x = 70o