In the given figure, $RT||SQ$. If $\angle QPS=110^{\circ}$, $\angle PQS=40^{\circ}$, $\angle PSR=75^{\circ}$ and $\angle QRS=65^{\circ}$, then find the value of $\angle QRT$"

Given: In the given figure, $RT||SQ$. If $\angle QPS=110^{\circ}$, $\angle PQS=40^{\circ}$, $\angle PSR=75^{\circ}$ and $\angle QRS=65^{\circ}$.

To do: To find the value of $\angle QRT$

Solution:

From the figure

In $\vartriangle PQS$,

$\angle PQS+\angle QPS+\angle PSQ=180^o$

$\Rightarrow \angle PSQ=180^o-\angle QPS-\angle PQS=180^o-100^o-40^o=40^o$

Given $\angle PSR=85^o $

$\Rightarrow \angle PSQ+\angle QSR=85^o$

$\Rightarrow \angle QSR=85^o-\angle PSQ=85^o-40^o =45^o$

In $\vartriangle QSR$

$\angle QRS+\angle PSQ+\angle SQR=180^o$

$\angle SQR=180^o-\angle QRS-\angle QSR=180^o-70^o-45^o =65^o$

AS $RT||SQ$

$\angle QRT=\angle SQR=65^o$      [$\because$ alternative angles]

Tutorialspoint

Updated on: 10-Oct-2022

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