Question

In the figure given below.$AB$ is parallel to $CD$ what is $\angle XOY$

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

reffer image

given:$AB||CD$

to find:$\angle XOY$

construct: join points $A$ and $C$; set $\angle ACD={90}^o........\left(i\right)$

As $AB||CD;\angle CAB={90}^o$ [from $\left(i\right)$ ] [alternate interior angles are equal]

$\angle CYO={180}^o-\angle OYD$ [supplementary angles]

$\angle COY={180}^o-{35}^o$

$\angle CYO={145}^o.....\left(ii\right)$

$\therefore$ The total angles sum to make ${540}^o$ [$\because$ pentagon]

$\therefore \angle XOY+\angle OXA+\angle XAC+\angle ACY+\angle CYO={540}^o$

$\therefore \angle XOY={540}^o-{450}^o$

$\therefore \angle XOY={90}^o$