https://file.aiquickdraw.com/mathbot/file/1727116245503xvq5sfqi.jpg

Let's work through the questions from the image, starting with each section in detail.

### 1–2:
The ray **PC** bisects ∠BPD, so it divides the angle into two equal parts.

1. If m∠CPD = 28°, then m∠BPC = 28°.
   - Since PC is the bisector, m∠BPC and m∠CPD are equal.

2. If m∠DPB = 62°, then m∠DPC = 62°.
   - Again, since PC is the bisector, both halves of ∠BPD are equal.

### 3–5:
In this section, **RU** bisects ∠TRV.

3. m∠TRV = 180°.
   - This is the total angle ∠TRV. 

4. m∠TRU = 90°.
   - Since **RU** is the bisector, each half is 90°.

5. m∠URV = 90°.
   - By symmetry from the bisector, m∠URV is also 90°.

### 6–9:
In this section, **BD** bisects ∠ABC.

6. To find **x**, we solve the equation:
   \[
   2x + 5 = 15.
   \]
   Subtracting 5 from both sides:
   \[
   2x = 10.
   \]
   Dividing by 2:
   \[
   x = 5.
   \]

7. m∠ABC = 30°.
   - Since BD is the bisector and x = 5, m∠ABC = 2 × (2x + 5) = 2 × 15°.

8. m∠DBC = 15°.
   - Since BD is the bisector, the angle is half of m∠ABC, so m∠DBC = 15°.

9. m∠ABD = 15°.
   - This is equal to m∠DBC since BD bisects ∠ABC.

### 10–14 (Angle Addition Practice):
Looking at the diagram:

10. m∠SVR = 70°.
   - Directly given.

11. m∠PVR = 160°.
   - Directly given.

12. m∠SVQ = 100°.
   - Directly given.

13. m∠SVP = 70° + 100° = 170°.
   - The sum of m∠SVR and m∠SVQ.

14. m∠RVQ = 160° − 100° = 60°.
   - m∠RVQ is the difference between m∠PVR and m∠SVQ.

### 15–18:
For these problems, use the given angle measures:

15. m∠BTE = 40.6°, m∠ETM = 60°.
    - m∠BTM = 40.6° + 60° = 100.6°.

16. m∠BTE = 112°.
    - m∠ETM = 168.7° − 112° = 56.7°.
    - m∠BTM = 168.7° (given).

17. m∠BTE = 47.2°.
    - m∠ETM = 92° − 47.2° = 44.8°.

18. m∠BTM = x°, m∠BTE = y°.
    - We can solve for the missing angles based on the other information.

Would you like any more details on any specific question or a deeper breakdown of these solutions?

### 5 Related Questions:
1. How can you calculate an angle when only part of it is given?
2. What is the significance of an angle bisector in geometry?
3. How can the angle addition postulate be used in solving complex diagrams?
4. What is the relation between supplementary angles and bisected angles?
5. How do you determine the total angle when given bisected angle measures?

**Tip:** When solving for missing angles, always check if the angles are complementary, supplementary, or part of a bisected angle. This helps narrow down possible calculations.

Angle Bisector and Angle Addition worksheet exercises, including finding bisected angles, solving for unknown angles, and using angle addition postulate.

This exercise focuses on using the Angle Bisector Theorem and Angle Addition Postulate to find unknown angle measures in various geometric diagrams. Includes step-by-step solutions for bisected angles and solving equations to determine angle values.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation