Question

OC is the angle bisector of angle BOD and angle AOC is a right angle. Find the measure of angle AOE.

• A. ${130}^{\circ }$
• B. ${145}^{\circ }$
• C. ${140}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is D ${150}^{\circ }$

Since angle AOC is a right angle,
AOB + BOC = 90°
AOB + 42° = 90°
AOB = 90° – 42°
AOB = 48°

And since OC is the angle bisector of BOD,
BOC = COD
COD = 42°

So, angle AOE = AOB + BOC + COD + DOE
= 48° + 42° + 42° + 18°
= 150°