Given: Angles 1 and 2 are complementary m/1 = 36° 2 3 1. 21 and 22 are complementary given m21= 36 given m 36⁰+ m22 = 90° definition of complementary angles 22 and 23 are a linear pair mz2+mz3=180° given linear pairs theorem What is most likely being shown by the proof? A. m/1 + m/3 = 90° B. m/1 + m23 180° O c. m/3126⁰ OD. m/3 144° m22-54° subtraction property of equality 54" + m23= 180° substitution property of equality ?

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section: Chapter Questions
Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...
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**Title: Understanding Complementary and Linear Pair Angles**

*Given: Angles 1 and 2 are complementary.*

1. **m∠1 = 36°**
   - *Given*

2. **∠1 and ∠2 are complementary**
   - *Definition: Complementary angles add up to 90°.*

3. **36° + m∠2 = 90°**
   - *Using the definition of complementary angles.*

4. **m∠2 = 54°**
   - *Subtraction property of equality.*

5. **∠2 and ∠3 are a linear pair**
   - *Given: Linear pairs add up to 180°.*

6. **m∠2 + m∠3 = 180°**
   - *Linear pairs theorem.*

7. **54° + m∠3 = 180°**
   - *Substitution property of equality.*

8. **Conclusion:** 
   - Therefore, m∠3 = 126°.

**What is most likely being shown by the proof?**

- A. m∠1 + m∠3 = 90°
- B. m∠1 + m∠3 = 180°
- C. m∠3 = 126°
- D. m∠3 = 144°

**Correct Answer:** C. m∠3 = 126°
Transcribed Image Text:**Title: Understanding Complementary and Linear Pair Angles** *Given: Angles 1 and 2 are complementary.* 1. **m∠1 = 36°** - *Given* 2. **∠1 and ∠2 are complementary** - *Definition: Complementary angles add up to 90°.* 3. **36° + m∠2 = 90°** - *Using the definition of complementary angles.* 4. **m∠2 = 54°** - *Subtraction property of equality.* 5. **∠2 and ∠3 are a linear pair** - *Given: Linear pairs add up to 180°.* 6. **m∠2 + m∠3 = 180°** - *Linear pairs theorem.* 7. **54° + m∠3 = 180°** - *Substitution property of equality.* 8. **Conclusion:** - Therefore, m∠3 = 126°. **What is most likely being shown by the proof?** - A. m∠1 + m∠3 = 90° - B. m∠1 + m∠3 = 180° - C. m∠3 = 126° - D. m∠3 = 144° **Correct Answer:** C. m∠3 = 126°
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