question_answer

In the given figure, find the measure of \[~\angle RQT\] (exterior\[~\angle le\]), if \[PQ=QR\] and\[\angle QPR=50{}^\circ \]

A)  \[80{}^\circ \]                          

B)  \[135{}^\circ \]          

C)  \[100{}^\circ \]       

D)  \[110{}^\circ \]

Correct Answer: C

Solution :

(c): By property of isosceles \[\Delta le,\]the two \[\angle les\]shown are \[50{}^\circ \] \[\Rightarrow \,\,\angle x=180{}^\circ -50{}^\circ -50{}^\circ =80{}^\circ \] \[\Rightarrow \,\,\angle RQT=180{}^\circ -80{}^\circ =100{}^\circ \]