Question

In the given figure, angle PQR is an isosceles triangle with PQ=PR.If angle PQR=46°, then find angle QSR and angle QTR.

Answer 1

The answer is angle S is 88° and angle QTR is 92°

Answer 2

Answer:

∠QSR = 88°

∠QTR = 92°

Step-by-step explanation:

Since PQ = PR

⇒ ∠PQR = ∠PRQ ( Angle opposite to equal sides are equal)

∴ ∠PRQ = 46°

In ΔPQR, using angle sum property of a triangle

∠PQR + ∠PRQ + ∠RPQ = 180

⇒ ∠RPQ = 180 - 92

⇒ ∠RPQ = 88°

Now, ∠RPQ = ∠QSR ( Angle formed in the same segment are equal)

⇒ ∠QSR = 88°

Now, QSRT is an cyclic quadrilateral and the sum of opposite angles of a cyclic quadrilateral is supplementary.

⇒ ∠QTR + ∠QSR = 180

⇒ ∠QTR = 180 - 88

⇒ ∠QTR = 92°