Question

In the given figure :
if ∠PQS = 60°,
find∠QPR.

Answer 1

In ΔPQS,
PQ = QS                 ....(given)
⇒ ∠QSP = ∠QPS  ....(angles opposite to  two equal sides are equal)
Now, ∠PQS + QPS + ∠QPS = 180°
⇒ 60° + 2∠QSP = 180°
⇒ 2∠QSP = 120°
⇒ ∠QSP = 60°
⇒ ∠QPS = 60°
In ΔPRS,
PS = SR                   ....(given)
⇒ ∠PRS = ∠RPS    ....(angles opposite to two equal sides are equal)
By exterior angle property,
∠QSP = ∠RPS + ∠PRS
⇒ 60° = 2∠RPS
⇒ ∠RPS = 30°
Now,
∠QPR = ∠QPS + ∠RPS
= 60° + 30° = 90°.