### Which angle is congruent to ∠8? Select all that apply.The diagram provided features two parallel lines, $ e $ and $ f $, intersected by a transversal $ g $. The points of intersection form eight angles, labeled as follows:- On the upper line $ e $: - ∠1 and ∠2 above the line $ e $ - ∠3 and ∠4 below the line $ e $ - On the lower line $ f $: - ∠5 and ∠6 above the line $ f $ - ∠7 and ∠8 below the line $ f $The question requires identifying all the angles congruent to ∠8.### Answer Choices- A. ∠1- B. ∠2- C. ∠3- D. ∠4To determine congruent angles, consider the following relationships between angles formed by parallel lines and a transversal:- Corresponding Angles- Alternate Interior Angles- Alternate Exterior Angles- Consecutive Interior Angles### Explanation∠8 is located below line $ f $ and to the right of the transversal $ g $.- **Alternate Interior Angles**: These are angles on opposite sides of the transversal and inside the two parallel lines. ∠8 and ∠5 are alternate interior angles.- **Corresponding Angles**: These are angles in matching corners when two lines are crossed by another line (the transversal). ∠8 and ∠4 are corresponding angles.- **Alternate Exterior Angles**: Not applicable here for ∠8.- **Consecutive Interior Angles**: Not applicable here for ∠8.Therefore, angles congruent to ∠8 are:- ∠4 (according to the corresponding angles postulate)### ConclusionSelect the following:- D. ∠4

To write the angle that is congruent to angle 8

Answered: Which angle e 7, 3, 4 5/6 7/8 9. g O A.…

Math

Geometry

Which angle e 7, 3, 4 5/6 7/8 9. g O A. Z1 O B. 2 C. Z3 D. Z4

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

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.

Question

### Which angle is congruent to ∠8? Select all that apply.

The diagram provided features two parallel lines, $ e $ and $ f $, intersected by a transversal $ g $. The points of intersection form eight angles, labeled as follows:

- On the upper line $ e $:
- ∠1 and ∠2 above the line $ e $
- ∠3 and ∠4 below the line $ e $

- On the lower line $ f $:
- ∠5 and ∠6 above the line $ f $
- ∠7 and ∠8 below the line $ f $

The question requires identifying all the angles congruent to ∠8.

### Answer Choices
- A. ∠1
- B. ∠2
- C. ∠3
- D. ∠4

To determine congruent angles, consider the following relationships between angles formed by parallel lines and a transversal:

- Corresponding Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Consecutive Interior Angles

### Explanation

∠8 is located below line $ f $ and to the right of the transversal $ g $.

- **Alternate Interior Angles**: These are angles on opposite sides of the transversal and inside the two parallel lines. ∠8 and ∠5 are alternate interior angles.
- **Corresponding Angles**: These are angles in matching corners when two lines are crossed by another line (the transversal). ∠8 and ∠4 are corresponding angles.
- **Alternate Exterior Angles**: Not applicable here for ∠8.
- **Consecutive Interior Angles**: Not applicable here for ∠8.

Therefore, angles congruent to ∠8 are:

- ∠4 (according to the corresponding angles postulate)

### Conclusion
Select the following:
- D. ∠4

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