Question

As shown in above figure AB and CD are two parallel lines and a line XY passes through them and intersects AB at P & CD at Q. If $\angle DQX=x^{\circ }$ then $\angle APY=$ ___.

• A. $x^{\circ }$
• B. ${180}^{\circ }$
• C. $180-x^{\circ }$
• D. $90-x^{\circ }$

Answer 1

The correct option is A

$x^{\circ }$

Given $\angle DQX=x^{\circ }$

$\because \angle BPY$ and $\angle DQX$ are supplementary angles so $\angle BPY={180}^{\circ }-x^{\circ }$

$\angle BPY$ and $\angle APY$ are supplementary angles.

$\Rightarrow \angle BPY+\angle APY={180}^{\circ }$

$\Rightarrow {180}^{\circ }-x^{\circ }+\angle APY={180}^{\circ }\Rightarrow \angle APY=x^{\circ }$

Also, $\angle APY=\angle DQX=x^{\circ }$ (Since they are alternate interior angles)