Question

In the given figure, ΔPQR is an isosceles triangle with PQ = PR and m ∠PQR = 35°. Find m ∠QSR and m ∠QTR.

Answer 1

Disclaimer: Figure given in the book was showing m∠PQR as m∠SQR.  It is given that ΔPQR is an isosceles triangle with PQ = PR and m∠PQR = 35°

 

We have to find the m∠QSR and m∠QTR

Since ΔPQR is an isosceles triangle

So ∠PQR = ∠PRQ = 35° 

Then

`angle QPR = 180° - (anglePQR + anglePRQ)`

                   = 180° - (35° + 35°)

                  =180° - 70°

                  =110°

Since PQTR is a cyclic quadrilateral

So

`angleP + angleT = 180°`

          `angle T = 180° - 110°` 

                        = 70°

In cyclic quadrilateral QSRT we have

`angle S + angle T` = 180°

          `angle S = 180° - 70°`

                 = 110°

Hence,

`m angleQSR `= 110° and  `angleQTR` = 70°