Question

Complete.

$m\angle DOB=\underset{¯}{?}$

Short answer

The complete statement is: $m\angle DOB=100°$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

From the given diagram it can be noticed that:

$\angle AOF=40°$and$\angle BOC=60°$

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 COD and AOF.

From the diagram, it can be noticed that:

The angles $COD$and $AOF$are vertically opposite angles.

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

Therefore, $\angle COD\cong \angle AOF$.

Therefore, $\angle COD=\angle AOF=40°$.

Therefore, the measure of the angle $COD$is $40°$.

Step 5. Find the value of the angle DOB.

From the given diagram it can be noticed that:

$\angle DOB=\angle COD+\angle BOC$

Therefore,

$\angle DOB=\angle COD+\angle BOC$

$=40+60$

$=100$

Therefore, the measure of the angle $DOB$is $100°$.

Step 6. Complete the given statement.

The measure of the angle $DOB$is $100°$.

Therefore, the complete statement is: $m\angle DOB=100°$.