Which of the following illustrations is a counterexample to the statement "Vertical angles are never complementary angles." A. В. .06 90° .06 06 С. 45 45 45 45 D. 90
Which of the following illustrations is a counterexample to the statement "Vertical angles are never complementary angles." A. В. .06 90° .06 06 С. 45 45 45 45 D. 90
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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Question
2. **Illustration B**
- This diagram shows a vertical angle of 90° at the intersection of two lines and another angle also of 90°. These are not complementary as complementary angles sum to 90°, whereas these sum to 180°.
3. **Illustration C**
- This diagram shows two intersecting lines forming angles of 45° each. Since 45° + 45° = 90°, these angles are complementary and hence provide the counterexample to the given statement.
4. **Illustration D**
- This diagram shows vertical angles of 45° each at the intersection of two lines. Since 45° + 45° = 90°, these are complementary angles, providing another counterexample to the given statement.
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In conclusion, **Illustrations C and D** are counterexamples to the statement "Vertical angles are never complementary angles" because they demonstrate instances where vertical angles add up to 90°, thereby being complementary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7245aef9-c798-4f68-8116-7b90c3c18a0a%2F4450bbee-ee0b-4e30-a5a6-3cdbe71fe0d3%2Fkhlp3jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Vertical and Complementary Angles
#### Question
Which of the following illustrations is a counterexample to the statement "Vertical angles are never complementary angles."
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#### Illustrations and Explanations
1. **Illustration A**
- This diagram shows two lines intersecting, forming vertical angles of 90° each. Since 90° + 90° = 180° (not 90°), these angles are not complementary.
2. **Illustration B**
- This diagram shows a vertical angle of 90° at the intersection of two lines and another angle also of 90°. These are not complementary as complementary angles sum to 90°, whereas these sum to 180°.
3. **Illustration C**
- This diagram shows two intersecting lines forming angles of 45° each. Since 45° + 45° = 90°, these angles are complementary and hence provide the counterexample to the given statement.
4. **Illustration D**
- This diagram shows vertical angles of 45° each at the intersection of two lines. Since 45° + 45° = 90°, these are complementary angles, providing another counterexample to the given statement.
---
In conclusion, **Illustrations C and D** are counterexamples to the statement "Vertical angles are never complementary angles" because they demonstrate instances where vertical angles add up to 90°, thereby being complementary.
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