Question

The measure of $\angle AOE$ is:

• A. ${40}^{\circ }$
• B. ${45}^{\circ }$
• C. ${50}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

According to the diagram:
$\angle DOA$ and $\angle BOC$ are vertically opposite angles
$\Rightarrow \angle DOA=\angle BOC={100}^{\circ }$
Also, $\angle FOD,\angle DOA,\angle AOE$ lie on the same straight line $EF$
$\Rightarrow \angle FOD+\angle DOA+\angle AOE={180}^{\circ }$
$\Rightarrow {35}^{\circ }+{100}^{\circ }+\angle AOE=180\circ$
$\Rightarrow \angle AOE={180}^{\circ }-{135}^{\circ }={45}^{\circ }$