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measure of an angle and its complement are in the ratio 4:11. Find the measure of the two angle

measure of an angle and its complement are in the ratio 4:11. Find the measure of the two angle

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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### Problem Statement The measure of an angle and its complement are in the ratio 4:11. Find the measure of the two angles. ### Solution To find the measures of the two angles, follow these steps: 1. **Understand the Concept of Complementary Angles**: Complementary angles are two angles whose measures add up to 90 degrees. 2. **Set Up the Equation**: Let the measure of the first angle be \( 4x \) and the measure of the second angle be \( 11x \), since they are in the ratio 4:11. 3. **Form the Equation**: Since the two angles are complementary, their measures add up to 90 degrees: \[ 4x + 11x = 90 \] 4. **Solve for \( x \)**: \[ 15x = 90 \quad \Rightarrow \quad x = \frac{90}{15} \quad \Rightarrow \quad x = 6 \] 5. **Find the Measures of the Angles**: - The measure of the first angle is \( 4x = 4 \times 6 = 24 \) degrees. - The measure of the second angle is \( 11x = 11 \times 6 = 66 \) degrees. ### Conclusion Thus, the measures of the two complementary angles are 24 degrees and 66 degrees.
Transcribed Image Text:### Problem Statement The measure of an angle and its complement are in the ratio 4:11. Find the measure of the two angles. ### Solution To find the measures of the two angles, follow these steps: 1. **Understand the Concept of Complementary Angles**: Complementary angles are two angles whose measures add up to 90 degrees. 2. **Set Up the Equation**: Let the measure of the first angle be \( 4x \) and the measure of the second angle be \( 11x \), since they are in the ratio 4:11. 3. **Form the Equation**: Since the two angles are complementary, their measures add up to 90 degrees: \[ 4x + 11x = 90 \] 4. **Solve for \( x \)**: \[ 15x = 90 \quad \Rightarrow \quad x = \frac{90}{15} \quad \Rightarrow \quad x = 6 \] 5. **Find the Measures of the Angles**: - The measure of the first angle is \( 4x = 4 \times 6 = 24 \) degrees. - The measure of the second angle is \( 11x = 11 \times 6 = 66 \) degrees. ### Conclusion Thus, the measures of the two complementary angles are 24 degrees and 66 degrees.
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