question_answer

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

A) \[{{155}^{o}}\]                                  

B) \[{{150}^{o}}\]

C) \[{{135}^{o}}\]                        

D)        \[{{95}^{o}}\]

Correct Answer: C

Solution :

 Here\[\angle QPL+\angle PLR={{180}^{o}}\]             \[\angle PLR={{180}^{o}}-\angle QPL\]             \[={{180}^{o}}-{{115}^{o}}={{65}^{o}}\]             \[\angle RLP=\angle LRT+\angle RTL\]             \[\angle LRT=\angle RLP-\angle RTL\]             \[={{65}^{o}}-{{20}^{o}}={{45}^{o}}\]             \[\angle SRT+\angle LRT={{180}^{o}}\]             \[\angle SRT={{180}^{o}}-\angle LRT\]             \[={{180}^{o}}-{{45}^{o}}={{135}^{o}}\]             \[\angle SRT={{135}^{o}}\]