Chapter 2: Q14. (page 52)

In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , role="math" localid="1649220811185" $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
width="69" height="20" role="math">m∠ZOW

Short Answer

Expert verified

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

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 $35 °$ .

Step 6. Find the measure of the angle ZOW.

From the given diagram it can be noticed that:

$∠ Z O W = ∠ Z O Y + ∠ Y O W$

Therefore,

$∠ Z O W = ∠ Z O Y + ∠ Y O W = 35 ° + 120 ° = 155 °$

Therefore, the measure of the angle $Z O W$ is $155 °$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , role="math" localid="1649220811185" $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
width="69" height="20" role="math">m∠ZOW

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.

Step 6. Find the measure of the angle ZOW.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Geometry

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the diagram, OT↔bisects ∠SOU, role="math" localid="1649220811185" m∠UOV=35, and m∠YOW=120. Find the measure of each angle.width="69" height="20" role="math">m∠ZOW

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.

Step 6. Find the measure of the angle ZOW.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Geometry

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the diagram, $\overset{\leftrightarrow}{O T}$ bisects $∠ S O U$ , role="math" localid="1649220811185" $m ∠ U O V = 35$ , and $m ∠ Y O W = 120$ . Find the measure of each angle.
width="69" height="20" role="math">m∠ZOW