Question

Consider the following figure:

Lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{XY}$ intersect in point O.

Find the value of (y – x).

• A. 40°
• B. 100°
• C. 140°
• D. Data insufficient

Answer 1

The correct option is B

100°

$\angle$AOX and $\angle$YOB are vertically opposite angles, and are therefore equal.
i.e., x = ${40}^{\circ }$
Also, $\angle$AOX and $\angle$XOB form a linear pair.
i.e., ${40}^{\circ }$ + $\angle$XOB = ${180}^{\circ }$
or, $\angle$XOB = y = ${140}^{\circ }$
therefore, y - x = ${140}^{\circ }$ - ${40}^{\circ }$
= ${100}^{\circ }$