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