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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
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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### Understanding Vertical and Complementary Angles #### Question Which of the following illustrations is a counterexample to the statement "Vertical angles are never complementary angles." --- #### 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. ![Diagram A](link_to_image_A) 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°. ![Diagram B](link_to_image_B) 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. ![Diagram C](link_to_image_C) 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. ![Diagram D](link_to_image_D) --- 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.
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." --- #### 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. ![Diagram A](link_to_image_A) 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°. ![Diagram B](link_to_image_B) 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. ![Diagram C](link_to_image_C) 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. ![Diagram D](link_to_image_D) --- 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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