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.

$m\angle SOU$

Short answer

The measure of the angle $\angle SOU$ is $120°$.

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 SOU and YOW.

From the diagram it can be noticed that:

The angles $SOU$and $YOW$are vertically opposite angles.

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

Therefore, $\angle SOU\cong \angle YOW$.

Step 5. Find the measure of the angle SOU.

As, $\angle SOU\cong \angle YOW$, therefore, $\angle SOU=\angle YOW$

Therefore, $\angle SOU=\angle YOW=120°$.

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