Question

Complete.

$m\angle COE=\underset{¯}{?}$

Short answer

The complete statement is: $m\angle COE=120°$.

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.

Theorem 2-3 states that the vertical angles are congruent.

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

From the diagram, it can be noticed that:

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

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

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

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

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

Step 5. Write the relation between the angles EOF and COE.

The angles $EOF$and form the linear pair.

Therefore, the sum of the angles $EOF$and $COE$is 180.

Therefore, $\angle EOF+\angle COE=180$.

Step 6. Find the value of the angle COE.

$\angle EOF+\angle COE=180$

$60+\angle COE=180$

$\angle COE=180-60$

$\angle COE=120$

Therefore, the measure of the angle $COE$is $120°$.

Step 7. Complete the given statement.

The measure of the angle $COE$is $120°$.

Therefore, the complete statement is: $m\angle COE=120°$.