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

Explanation

Δ PQR is isosceles
∴∠PRQ = 30^o
Also in Δ PQR
^{^}Q = 180 -(30 + 30)
= 120^o
PQRS is a cyclic quad
∴^{^}S + ^{^}Q = 180(opp ∠s of a cyclic quad)
S + 120 = 180
S = 60^o
In ΔPSR
x + 50 + 60
= 180(sum of ∠s of a Δ)
x + 110 = 180
x = 180 - 110
x = 70^o

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