Chapter 2: Q13. (page 52)

In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
$m ∠ Z O Y$

Short Answer

Expert verified

The measure of the angle $∠ Z O Y$ 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 $∠ A ≅ ∠ B$ .

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 $Z O Y$ and $U O V$ are vertically opposite angles.

Therefore, from the theorem 2-3, it can be said that the angles $Z O Y$ and $U O V$ are congruent angles.

Therefore, $∠ Z O Y ≅ ∠ U O V$ .

Step 5. Find the measure of the angle ZOY.

As, $∠ Z O Y ≅ ∠ U O V$ , therefore, $∠ Z O Y = ∠ U O V$

Therefore, $∠ Z O Y = ∠ U O V = 35 °$ .

Therefore, the measure of the angle $Z O Y$ is $35 °$ .

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In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
$m ∠ Z O Y$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of congruent angles.

Step 3. Write the theorem 2-3.

Step 4. Write the relations between the angles ZOY and UOV.

Step 5. Find the measure of the angle ZOY.

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In the diagram, OT↔bisects ∠SOU, m∠UOV=35, and m∠YOW=120. Find the measure of each angle.m∠ZOY

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Definition of congruent angles.

Step 3. Write the theorem 2-3.

Step 4. Write the relations between the angles ZOY and UOV.

Step 5. Find the measure of the angle ZOY.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
$m ∠ Z O Y$