question_answer

\[\text{QP}|\,\,|TS\] and \[\angle QRS=36{}^\circ ,\] then value of \[\angle PQR\]

A)  \[48{}^\circ \]                                  

B)  \[52{}^\circ \]

C)  \[72{}^\circ \]               

D)  \[50{}^\circ \]

Correct Answer: C

Solution :

    Draw a line UR parallel to QP \[\angle PQR=\angle QRU=x\] \[\angle QRS+\angle SRU=x\] \[\angle SRU=x-36{}^\circ \] \[\angle TSR+\angle SRU=180{}^\circ \] \[2x+x-36{}^\circ =180{}^\circ \] \[3x=180{}^\circ +36{}^\circ =216\] \[x=72{}^\circ \]