Question

In the diagram, $\overleftrightarrow{OT}$bisects $\angle SOU$, role="math" localid="1649220811185" $m\angle UOV=35$, and $m\angle YOW=120$. Find the measure of each angle.

width="69" height="20" role="math">m∠ZOW

Short answer

The measure of the angle $\angle ZOW$is $155°$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

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 ZOY and UOV.

From the diagram it can be noticed that:

The angles $ZOY$and $UOV$are vertically opposite angles.

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

Therefore, $\angle ZOY\cong \angle UOV$.

Step 5. Find the measure of the angle ZOY.

As, $\angle ZOY\cong \angle UOV$, therefore, $\angle ZOY=\angle UOV$

Therefore, $\angle ZOY=\angle UOV=35°$.

Therefore, the measure of the angle $ZOY$is $35°$.

Step 6. Find the measure of the angle ZOW.

From the given diagram it can be noticed that:

$\angle ZOW=\angle ZOY+\angle YOW$

Therefore,

$$\begin{gathered} \angle ZOW=\angle ZOY+\angle YOW \\ =35°+120° \\ =155° \end{gathered}$$

Therefore, the measure of the angle $ZOW$is $155°$.