Question

Based on the given figure, which of the following statements is true?

• A. $\angle 5$ and $\angle 7$ are supplementary angles.
• B. $\angle 7={55}^{\circ }$
• C. $\angle 8$ and $\angle 1$ are corresponding angles.
• D. $\angle 4$ and $\angle 5$ are alternate angles.

Answer 1

The correct option is D $\angle 4$ and $\angle 5$ are alternate angles.

$\angle 5$ and $\angle 7$ are vertically opposite angles.

$\angle 6={55}^{\circ }$ (Alternate angles)

$\angle 7+\angle 6={180}^{\circ }$ (Adjacent angle on straight line)

$\Rightarrow \angle 7+{55}^{\circ }={180}^{\circ }\Rightarrow \angle 7={125}^{\circ }$

$\angle 1$ and $\angle 8$ are not corresponding angles.

$\angle 4$ and $\angle 5$ are alternate angles.

So only option $D$ is correct.