Mathematics

In the diagram above, if ∠RPS = 50o, ∠RPQ = 30o and PQ = QR,…

In the diagram above, if ∠RPS = 50o, ∠RPQ = 30o and PQ = QR, find the value of ∠PRS.
  • A.
    80o
  • B.
    70o
  • C.
    60o
  • D.
    50o
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