question_answer

In the given figure, PQ|| RS. The value of x is

A)  \[50{}^\circ \] 

B)  \[80{}^\circ \]   

C)  \[75{}^\circ \] 

D)  \[65{}^\circ \]

Correct Answer: A

Solution :

Draw, AB || PQ \[\angle ATP=\angle TPQ=50{}^\circ \]and\[\angle BTR+\angle TRS=180{}^\circ \]                         \[\angle BTR=80{}^\circ \] and \[\angle ATP+x+\angle BTR=180{}^\circ \] \[\therefore \]      \[x=180{}^\circ -\,\,(50{}^\circ +80{}^\circ )=50{}^\circ \]