question_answer

Assume \[p|\,\,\,|q\] in the figure shown. Then 'x' equals.

A)  \[18{}^\circ \]                                  

B)  \[22{}^\circ \]

C)  \[62{}^\circ \]                      

D)  \[72{}^\circ \]

Correct Answer: C

Solution :

    Draw a ray rs parallel to pp' and qq' \[\angle o=140{}^\circ ,\,\,\angle o'=158{}^\circ \](Opposite angles) \[\angle p'or+\angle ors=180{}^\circ (pp'||qq',co\text{-}\operatorname{int}\,\text{angles})\] and \[\angle q'o'r+\angle o'rs=180{}^\circ \]          \[(pp'||qq',co\text{-}\operatorname{int}\,\text{angles})\] adding \[\angle p'or+\angle ors+\angle q'o'r+\angle o'rs=360{}^\circ \] \[140{}^\circ +\angle ors+158{}^\circ \angle o'rs=360{}^\circ \] \[\angle ors+\angle o'rs=360{}^\circ -298{}^\circ =62{}^\circ \] \[\angle x=62{}^\circ \]