Question

In the given figure, lines $AB$ and $CD$ are parallel to each other and
$\angle FMB$ is equal to ${75}^{\circ }.$ Which of the following statements is true?

• A. $\angle AME$ and $\angle BME$ are complementary angles.
• B. $\angle AMF$ and $\angle BME$ are supplementary angles.
• C. $\angle AMF$ and $\angle BME$ are complementary angles.
• D. $\angle AME$ and $\angle BME$ are supplementary angles.

Answer 1

The correct option is D $\angle AME$ and $\angle BME$ are supplementary angles.

In the given figure, we can observe:
$\angle FMB+\angle BME={180}^{\circ }$ (supplementary angles)
$\Rightarrow {75}^{\circ }+\angle BME={180}^{\circ }$
$\Rightarrow \angle BME={180}^{\circ }-{75}^{\circ }={105}^{\circ }$

$\angle AME=\angle BMF={75}^{\circ }$ (vertical angles)
$\angle AMF=\angle BMF={75}^{\circ }+{105}^{\circ }={180}^{\circ }$
Therefore, $\angle AME$ and $\angle BME$ are supplementary angles.