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.
$\therefore x={40}^{\circ }$
Also, $\angle AOX$ and $\angle XOB$ form a linear pair.
$\therefore {40}^{\circ }+\angle XOB={180}^{\circ }$
$\Rightarrow \angle XOB=y={140}^{\circ }$
$\therefore y-x={140}^{\circ }-{40}^{\circ }$
$={100}^{\circ }$