Question

Given:17 | 12, tı || tz, and mZ1 = 123º Prove: m_3 = 57° Complete the two-column proof below?

Answer 1

In order to prove that m_3 is 57°, you can use a two-column proof. Start by stating the given information and then use the definition of angles and the fact that the sum of angles in a triangle is 180°. Substitute the value of mZ1 into the equation and solve for m_3, which is 57°.

Step-by-step explanation:

Two-Column Proof:

Statements

1. 
   
3. mZ1 = 123°
4. 
   
6. Angles are defined as positive in the counter clockwise direction
7. 
   
9. m_3 = 180° - mZ1 (Sum of angles in a triangle is 180°)
10. 
    
12. m_3 = 180° - 123°
13. 
    
15. m_3 = 57°

Reasons

1. 
   
3. Given
4. 
   
6. Definition of angles
7. 
   
9. Sum of angles in a triangle
10. 
    
12. Substitution
13. 
    
15. Solving for m_3

Learn more about Triangle angles