Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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Question
![## Transversals and Angle Measurements Practice
### Instructions:
Use the diagram to find all of the missing angles, knowing that \(a \parallel b\).
### Diagram Description:
The diagram features two parallel lines, \(a\) and \(b\), which are intersected by two transversals forming various angles. Notable angles include:
- \(\angle 3 = 54^\circ\)
- \(\angle 8 = 67^\circ\)
These angles are used to find the measurements of the other labeled angles in the diagram.
### Labels and Diagram:
```
(arrow a) ------ 1 -- 2 ----------- 4 -- 5 ------------------- (arrow a)
| / \
| / \
| 6 / 7 \
3 \ 54^\circ 67^\circ / 8
| / 10 \
| / \
| 12 / \ 9
| / \
(arrow b) ------ 11 -- 10 --------- 8 -- 9 ---------------- (arrow b)
```
### Tasks:
Determine the following angles:
- \(\angle 1\) = \(\_\_\_)^\circ
- \(\angle 2\) = \(\_\_\_)^\circ
- \(\angle 3\) = \(\_\_\_)^\circ
- \(\angle 4\) = \(\_\_\_)^\circ
Fill in the boxes with the correct values deduced from the given angles and the properties of parallel lines and transversals.
### Solution Explanation:
Using the properties of corresponding angles, alternate interior angles, and vertical angles, explain how you determined the missing angles.
Note: The parallel relationship between lines \(a\) and \(b\) is critical to solving for the unknown angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0449a0b2-b573-4c37-a73f-7ccfb17fc319%2Fd3b7132d-bf4c-4883-9e75-29de65eda60b%2Fdw3wm2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Transversals and Angle Measurements Practice
### Instructions:
Use the diagram to find all of the missing angles, knowing that \(a \parallel b\).
### Diagram Description:
The diagram features two parallel lines, \(a\) and \(b\), which are intersected by two transversals forming various angles. Notable angles include:
- \(\angle 3 = 54^\circ\)
- \(\angle 8 = 67^\circ\)
These angles are used to find the measurements of the other labeled angles in the diagram.
### Labels and Diagram:
```
(arrow a) ------ 1 -- 2 ----------- 4 -- 5 ------------------- (arrow a)
| / \
| / \
| 6 / 7 \
3 \ 54^\circ 67^\circ / 8
| / 10 \
| / \
| 12 / \ 9
| / \
(arrow b) ------ 11 -- 10 --------- 8 -- 9 ---------------- (arrow b)
```
### Tasks:
Determine the following angles:
- \(\angle 1\) = \(\_\_\_)^\circ
- \(\angle 2\) = \(\_\_\_)^\circ
- \(\angle 3\) = \(\_\_\_)^\circ
- \(\angle 4\) = \(\_\_\_)^\circ
Fill in the boxes with the correct values deduced from the given angles and the properties of parallel lines and transversals.
### Solution Explanation:
Using the properties of corresponding angles, alternate interior angles, and vertical angles, explain how you determined the missing angles.
Note: The parallel relationship between lines \(a\) and \(b\) is critical to solving for the unknown angles.
![### Measurement of Angles
The following exercise is aimed at helping you practice evaluating the provided angles. You will fill in the boxes with the measured angle in degrees (°).
1. \( \angle 1 \) = [ ]°
2. \( \angle 2 \) = [ ]°
3. \( \angle 3 \) = [ ]°
4. \( \angle 4 \) = [ ]°
5. \( \angle 5 \) = [ ]°
6. \( \angle 6 \) = [ ]°
7. \( \angle 7 \) = [ ]°
8. \( \angle 8 \) = [ ]°
9. \( \angle 9 \) = [ ]°
10. \( \angle 10 \) = [ ]°
11. \( \angle 11 \) = [ ]°
12. \( \angle 12 \) = [ ]°
**Instructions:**
- Measure each angle using a protractor or an angle-measuring tool.
- Record the measured value in the box next to the corresponding angle number.
This exercise will aid you in understanding and practicing how to measure and record angles accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0449a0b2-b573-4c37-a73f-7ccfb17fc319%2Fd3b7132d-bf4c-4883-9e75-29de65eda60b%2Far88ra9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Measurement of Angles
The following exercise is aimed at helping you practice evaluating the provided angles. You will fill in the boxes with the measured angle in degrees (°).
1. \( \angle 1 \) = [ ]°
2. \( \angle 2 \) = [ ]°
3. \( \angle 3 \) = [ ]°
4. \( \angle 4 \) = [ ]°
5. \( \angle 5 \) = [ ]°
6. \( \angle 6 \) = [ ]°
7. \( \angle 7 \) = [ ]°
8. \( \angle 8 \) = [ ]°
9. \( \angle 9 \) = [ ]°
10. \( \angle 10 \) = [ ]°
11. \( \angle 11 \) = [ ]°
12. \( \angle 12 \) = [ ]°
**Instructions:**
- Measure each angle using a protractor or an angle-measuring tool.
- Record the measured value in the box next to the corresponding angle number.
This exercise will aid you in understanding and practicing how to measure and record angles accurately.
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