Question

If BD is the angle bisector of $\angle ABC$ (which measures ${30}^{\circ }),$ then what is the measure of $\angle ABD$?

• A. ${30}^{\circ }$
• B. ${20}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is D ${15}^{\circ }$

An angle bisector is a ray or line that divides an angle into two equal angles.


Given:
BD is the angle bisector of $\angle ABC.$

$⟹$ BD divides $\angle ABC$ into two equal angles: $\angle ABD$ and $\angle DBC.$

$⟹\angle ABD=\angle DBC=\frac{1}{2}\times \angle ABC=\frac{1}{2}\times {30}^{\circ }={15}^{\circ }$

$\therefore \angle ABD={15}^{\circ }$