Question

The measure of the obtuse $\angle EOF$ is:

• A. ${110}^{\circ }$
• B. ${105}^{\circ }$
• C. ${100}^{\circ }$

Answer 1

The correct option is B ${105}^{\circ }$

Given the diagram:

Let us first construct a line $QOP$ (from left to right) parallel to lines $BA$ and $DC$.

Clearly, we can say that:
$\angle FOQ+\angle BFO={180}^{\circ }$ (co-interior angles)
$\Rightarrow \angle FOQ={180}^{\circ }-{105}^{\circ }={75}^{\circ }$
Also, $\angle CEO$ and $\angle EOQ$ are alternate interior angles.
$\Rightarrow \angle CEO=\angle EOQ={30}^{\circ }$
Now, $\angle EOF=\angle FOQ+\angle EOQ$
$\Rightarrow \angle EOF={75}^{\circ }+{30}^{\circ }={105}^{\circ }$