Question

In the diagram, $\overleftrightarrow{\mathit{O}\mathit{T}}$bisects $\angle SOU$, $m\angle UOV=35$, and $m\angle YOW=120$. Find the measure of each angle.

$m\angle ZOY$

Short answer

The measure of the angle $\angle ZOY$is $35°$.

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 $35°$.