Question

In the figure shown, lines l and m are parallel and lines r and t are transversals. Find x.

• A. ${45}^{\circ }$
• B. ${75}^{\circ }$
• C. ${60}^{\circ }$
• D. ${105}^{\circ }$

Answer 1

The correct option is A

${45}^{\circ }$

$\angle AOC+{105}^{\circ }={180}^{\circ }$ [Co-interior angles]

Hence, $\angle AOC={180}^{\circ }-{105}^{\circ }={75}^{\circ }$

$\angle AOB={120}^{\circ }$ [Corresponding angles]

$\angle AOB=\angle AOC+\angle BOC$

$\Rightarrow {120}^{\circ }={75}^{\circ }+x$

$\Rightarrow x={120}^{\circ }-{75}^{\circ }={45}^{\circ }$