2000
Mathematics
67ca00ce0c643c71d77dee1f
In the diagram above, if ∠RPS = 50°, ∠RPQ = 30° and PQ = QR, find the value of ∠PRS.
A.
80°
B.
70°
C.
60°
D.
50°
Correct Answer: 70°
Explanation
Δ PQR is isosceles ∴∠PRQ = 30° Also in Δ PQR ^Q = 180 -(30 + 30) = 120° PQRS is a cyclic quad ∴^S + ^Q = 180(opp ∠s of a cyclic quad) S + 120 = 180 S = 60° In ΔPSR x + 50 + 60 = 180(sum of ∠s of a Δ) x + 110 = 180 x = 180 - 110 x = 70°
Δ PQR is isosceles ∴∠PRQ = 30° Also in Δ PQR ^Q = 180 -(30 + 30) = 120° PQRS is a cyclic quad ∴^S + ^Q = 180(opp ∠s of a cyclic quad) S + 120 = 180 S = 60° In ΔPSR x + 50 + 60 = 180(sum of ∠s of a Δ) x + 110 = 180 x = 180 - 110 x = 70°THIS WEEK's
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