Question

If ZY || WX in the following figure, find the measure of ∠x.

• A. 112°
• B. 56°
• C. 68°
• D. 106°

Answer 1

The correct option is A 112°

Given: ZY || WX
$\Rightarrow \angle YWX=\angle ZYW={28}^{\circ }$
[∵ Alternate interior angles are equal]

Angle sum property of a triangle tells that sum of three interior angles of a triangle is equal to 180°.

In △WOX,
By angle sum property,
$\angle OWX+\angle WXO+\angle XOW={180}^{\circ }$
$\Rightarrow x={180}^{\circ }-({40}^{\circ }+{28}^{\circ })$
$\Rightarrow x={180}^{\circ }-{68}^{\circ }={112}^{\circ }$