question_answer

In the given figure. If \[\mathbf{PQ}\parallel \mathbf{RS},\mathbf{ZQPT}=\mathbf{11}{{\mathbf{5}}^{{}^\circ }}\] and \[\angle \mathbf{PTR}=\mathbf{1}{{\mathbf{5}}^{{}^\circ }}\], then \[\angle \mathbf{SRT}\] is equal to:

A)  \[{{145}^{{}^\circ }}\]                     

B)  \[{{150}^{{}^\circ }}\]

C)  \[{{135}^{{}^\circ }}\]     

D)  \[{{100}^{{}^\circ }}\]

Correct Answer: C

Solution :

(c) Here \[\angle QPL+\angle PLR={{180}^{{}^\circ }}\] \[\angle PLR={{180}^{{}^\circ }}-\angle QPL\] \[{{180}^{{}^\circ }}-{{115}^{{}^\circ }}=65{}^\circ \] \[\angle RLP=\angle LRT+\angle RTL\] \[\angle LRT=\angle RLP-\angle RTL={{60}^{{}^\circ }}-{{15}^{{}^\circ }}={{45}^{{}^\circ }}\] \[\angle SRT+\angle RLP={{180}^{{}^\circ }}\] \[\angle SRT={{180}^{{}^\circ }}-\angle LRT={{180}^{{}^\circ }}-{{45}^{{}^\circ }}={{135}^{{}^\circ }}\] \[\angle SRT={{135}^{{}^\circ }}\]