In the figure,if $\angle PQR = \angle PRQ$,then prove that $\angle PQS = \angle PRT$.
(N/A) Since $ST$ is a straight line,
$\therefore \angle PQS + \angle PQR = 180^\circ$ ........... $(1)$
Similarly,$\angle PRT + \angle PRQ = 180^\circ$ ........... $(2)$
From $(1)$ and $(2)$,we have
$\angle PQS + \angle PQR = \angle PRT + \angle PRQ$
But $\angle PQR = \angle PRQ$ [Given]
$\therefore \angle PQS = \angle PRT$
$\therefore \angle PQS + \angle PQR = 180^\circ$ ........... $(1)$
Similarly,$\angle PRT + \angle PRQ = 180^\circ$ ........... $(2)$
From $(1)$ and $(2)$,we have
$\angle PQS + \angle PQR = \angle PRT + \angle PRQ$
But $\angle PQR = \angle PRQ$ [Given]
$\therefore \angle PQS = \angle PRT$
Explore More
Similar Questions
If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel,then prove that the two lines are parallel.
Medium
View SolutionIn the figure,lines $XY$ and $MN$ intersect at $O$. If $\angle POY = 90^o$ and $a: b = 2: 3$,find $c$. (in $^o$)
Medium
View SolutionIn the figure,find the values of $x$ and $y$ and then show that $AB \parallel CD$.
Medium
View SolutionIn the figure,if $PQ \parallel RS$,$\angle MXQ = 135^o$ and $\angle MYR = 40^o$,find $\angle XMY$. (in $^o$)
Medium
View SolutionIn the figure,the side $QR$ of $\Delta PQR$ is produced to a point $S$. If the bisectors of $\angle PQR$ and $\angle PRS$ meet at point $T$,then prove that $\angle QTR = \frac{1}{2} \angle QPR$.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo