Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![### Understanding the Relationship Between Angles
In the following geometric diagram, we are given certain angles and asked to determine others based on the given information:
#### Diagram Description:
- The diagram features two parallel lines intersected by a transversal line.
- Point A and Point D are where the transversal crosses the parallel lines.
- Angles are labeled as angles 1, 2, 3, and 4.
- We are given that \( \angle 3 = 40^\circ \).
#### Question:
Find the measure of \( \angle 2 \).
#### Solution:
1. **Identify the Given Information**:
- \( \angle 3 = 40^\circ \)
2. **Understanding Angle Relationships**:
- Since Angle 3 and Angle 2 are corresponding angles (formed by a transversal intersecting two parallel lines), they are equal.
Therefore, the measure of \( \angle 2 \) is:
\[ \angle 2 = 40^\circ \]
### Answer:
\[ \angle 2 = 40^\circ \]
If you need to input the answer, you can type "40" in the given field and press "Enter".
### Graphical Explanation:
- The diagram shows two parallel lines with a transversal intersecting them. Angle 3 is given as 40 degrees. The position of angle 2 corresponds to angle 3, thereby making angle 2 equal to 40 degrees as well.
---
It's important to use these properties of parallel lines and transversals to solve for unknown angles efficiently. Remember to apply the corresponding angles postulate in similar problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e7b1523-fbb7-48a7-b23c-2eac7de95669%2F10e44dc0-e945-4766-9797-0cc995ea22b1%2Fxrd74b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Relationship Between Angles
In the following geometric diagram, we are given certain angles and asked to determine others based on the given information:
#### Diagram Description:
- The diagram features two parallel lines intersected by a transversal line.
- Point A and Point D are where the transversal crosses the parallel lines.
- Angles are labeled as angles 1, 2, 3, and 4.
- We are given that \( \angle 3 = 40^\circ \).
#### Question:
Find the measure of \( \angle 2 \).
#### Solution:
1. **Identify the Given Information**:
- \( \angle 3 = 40^\circ \)
2. **Understanding Angle Relationships**:
- Since Angle 3 and Angle 2 are corresponding angles (formed by a transversal intersecting two parallel lines), they are equal.
Therefore, the measure of \( \angle 2 \) is:
\[ \angle 2 = 40^\circ \]
### Answer:
\[ \angle 2 = 40^\circ \]
If you need to input the answer, you can type "40" in the given field and press "Enter".
### Graphical Explanation:
- The diagram shows two parallel lines with a transversal intersecting them. Angle 3 is given as 40 degrees. The position of angle 2 corresponds to angle 3, thereby making angle 2 equal to 40 degrees as well.
---
It's important to use these properties of parallel lines and transversals to solve for unknown angles efficiently. Remember to apply the corresponding angles postulate in similar problems.
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