Question

In the given figure, $\angle x={20}^{\circ },\angle y={160}^{\circ },\angle w={105}^{\circ },\angle z={75}^{\circ }$

Which of the following is correct?

• A. Ray m and ray n are opposite rays
• B. Ray l and ray n are opposite rays
• C. Ray p and ray n are opposite rays
• D. Ray l and ray m are parallel

Answer 1

The correct option is B Ray l and ray n are opposite rays

Ray n and ray l contain two angles between them.
One of them is $\angle x+\angle y$ and the other is $\angle z+\angle w$
$\angle x+\angle y={20}^{\circ }+{160}^{\circ }={180}^{\circ }$
$\angle z+\angle w={75}^{\circ }+{105}^{\circ }={180}^{\circ }$

Thus, ray n and ray l form a straight line. Since they start from the same point and are a part of the same line, they are opposite rays.