Given: m∠1 = 62° Line l is parallel to line m Prove: m∠7 = 118°

Question

 Write a complete two-column proof for the following information.

Answer 1

As Mark commented, it is almost impossible to answer without a diagram. However, I am going to describe a particular situation and give you a proof. Let's call the transversal, the line that crosses l and m, line t. ∠1 lies above line l and to the left of line t. ∠7 lies below line m and to the left of line t. ∠6 lies above line m and to the left of line t.

 

Statements                                        Reasons                                                                     

1. l is parallel to m                              1. Given

2. ∠1 ≅ ∠6                                          2. If two parallel lines are cut by a transversal, then corresponding angles are ≅.

3. m∠1 = m∠6                                    3. If two angles are congruent, then they have the same measure.

4. m∠6 + m∠7 = 180º                         4. Two angles that form a straight line have a sum of 180º.

5. m∠1 + m∠7 = 180º                         5. Substitution Property

6. m∠1 = 62º                                      6. Given                                   

7. 62º + m∠7 = 180º                           7. Substitution

8. ∴ m∠7 = 118º                                  8. Subtraction Property