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In the figure, $\triangle PQR$ is an isosceles triangle with $PQ = PR$ and $m \angle PQR = 35^o$. Find $m \angle QSR$ and $m \angle QTR$.
"
Given:
In the figure, $\triangle PQR$ is an isosceles triangle with $PQ = PR$ and $m \angle PQR = 35^o$.
To do:
We have to find $m \angle QSR$ and $m \angle QTR$.
Solution:
$\angle PQR = 35^o$
This implies,
$\angle PRQ = 35^o$
$\angle PQR + \angle PRQ + \angle QPR = 180^o$ (Sum of angles of a triangle)
$35^o + 35^o + \angle QPR = 180^o$
$70^o + \angle QPR = 180^o$
$\angle QPR = 180^o - 70^o = 110^o$
$\angle QSR = \angle QPR$ (Angle in the same segment of circles)
$\angle QSR = 110^o$
$PQTR$ is a cyclic quadrilateral.
Therefore,
$\angle QTR + \angle QPR = 180^o$
$\angle QTR + 110^o = 180^o$
$\angle QTR = 180^o -110^o = 70^o$
Hence $\angle QTR = 70^o$.
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