Question

For an angle $\angle ABC={75}^o,BD$ is an angle bisector. Find the measure of adjacent angles.

• A. ${35}^o$
• B. ${37}^o$
• C. ${37.5}^o$
• D. ${37.8}^o$

Answer 1

The correct option is C ${37.5}^o$

Adjacent angles are the angles that share a common ray and a common vertex.

Draw an angle $\angle ABC={75}^o,$ and the angle bisector $BD$.

Angle bisector bisects the angle $\angle ABC$ in to two equal anlges.
$\angle ABD=\angle DBC$
$\Rightarrow \angle ABD=\frac{\angle ABC}{2}=\frac{{75}^o}{2}={37.5}^o$

Also, $\angle ABD$ and $\angle DBC$ are adjacent angles.
Hence, the measure of both the adjacent angles is ${37.5}^o$.