question_answer

In the given figure, if \[PQ||RS,\]\[\angle QPT=115{}^\circ \]and\[\angle PTR=20{}^\circ ,\]then \[\angle SRT\]is equal to

A)  \[155{}^\circ \]

B)  \[150{}^\circ \]

C)  \[135{}^\circ \]

D)  \[95{}^\circ \]

Correct Answer: C

Solution :

Here, \[\angle QPL+\angle PLR=180{}^\circ \]

\[\angle PLR=180{}^\circ -\angle QPL=180{}^\circ -115{}^\circ =65{}^\circ \]

\[\angle RLP=\angle LRT+\angle RTL\]

\[\angle LRT=\angle RLP-\angle RTL=65{}^\circ -20{}^\circ =45{}^\circ \]

\[\angle SRT+\angle LRT=180{}^\circ \]

\[\angle SRT=180{}^\circ -\angle LRT\]

\[\angle SRT=180{}^\circ -45{}^\circ =135{}^\circ \]

\[\angle SRT=135{}^\circ \]