Question

Angle bisector of a ${260}^{\circ }$ reflex angle also divides an obtuse angle into two acute angles. What is the measure of acute angle?

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${100}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is A ${50}^{\circ }$


Angle bisector $\text{CD}$ of reflex $\angle \text{AOB}$ i.e ${260}^{\circ }$ divides it into two equal obtuse angle of ${130}^{\circ }$ i.e $\angle \text{AOC}$ and $\angle \text{COB}$.

But, angle bisector $\text{CD}$ also divides an obtuse angle $\angle \text{AOB}$ of $(360-260{)}^{\circ }={100}^{\circ }$ measure into two equal acute angles $\angle \text{AOD}$ and $\angle \text{DOB}$ of ${50}^{\circ }$ each.

So, the measure of acute angles is ${50}^{\circ }$ each.