Question

Complete.

$m\angle FOE=\underset{¯}{?}$

Short answer

The complete statement is: $m\angle FOE=60°$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

From the given diagram it can be noticed that:

$\angle BOC=60°$

Step 2. Definition of congruent angles.

The two angles are said to be congruent angles if they have equal measure.

If two angles A and B are congruent then it can be written as $\angle A\cong \angle B$.

Step 3. Write the theorem 2-3.

The theorem 2-3 states that the vertical angles are congruent.

Step 4. Write the relations between the angles FOE and BOC.

From the diagram, it can be noticed that:

The angles $FOE$and $BOC$are vertically opposite angles.

Therefore, from theorem 2-3, it can be said that the angles $FOE$and $BOC$are congruent angles.

Therefore, $\angle FOE\cong \angle BOC$.

Therefore, $\angle FOE=\angle BOC=60°$.

Step 5. Complete the statement.

Therefore, the measure of the angle $FOE$is $60°$.

Therefore, the complete statement is: $m\angle FOE=60°$.