Question

In the figure given below, AB || CD. Calculate the value of x + y - z.

• A. ${90}^{\circ }$
• B. ${80}^{\circ }$
• C. ${50}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ }$

Sum of the interior angles on the same side of the transversal is 180°.
AB ∥ CD and PQ is the transversal
So, $\angle CQP+\angle APQ=180°$
$140°+x=180°$
$x=180°-140°$
$x=40°$
Similarly, AB ∥ CD and PR is the transversal
So, $\angle BPR+\angle DRP=180°$
$z+130°=180°$
$z=180°-130°$
$z=50°$

$x+y+z=180°$ [Linear pair of angles]
So,
$40°+y+50°=180°$
$y+90°=180°$
$y=180°-90°$
$y=90°$
$x+y-z=40°+90°-50°=80°$