Write a complete two-column proof for the following information. hint: use the angle addition theorem and the fact that a line is made up of two opposite rays.

given: m∠1 = 62° and lines t and l intersect
prove: m∠4 = 62°

needs to be a actual two column proof with statements and reasons. im just not really understanding it

Step-by-step explanation:

Given: m∠1 = 62° and lines t and l intersect

Prove: m∠4 = 62°

Proof:

Statement                                        Reason

m∠1 = 62°                                         Given

m∠1 , m∠2 are supplementary       t is a straight line hence linear pair.

m∠4 , m∠2 are supplementary       r is a straight line hence linear pair.

Angle 2=180-62 = 118                      Definition of supplementary angles

Angle 4 = 180-118 =62                     -do-

Angle 1 = Angle 4                            Equality property

Hence proved

   Statement                  Reason        

1. AB = x + 16                 1. Given

  BC = 4x + 11

   AC = 77

2. AB + BC = AC             2. Segment Addition Postulate

3. x + 16 + 4x + 11 = 77     3. Substitution Property

4. 5x + 27 = 77                 4. Simplification (added like terms)

5. 5x = 50                         5. Subtraction Property of Equality

6. x = 10                             6. Division Property of Equality

7. AB = 10 + 16                   7. Substitution Property

8. AB = 26                          8. Simplification (added like terms)

m∠1 = 62°                                         Given

m∠1 , m∠2 are supplementary       t is a straight line hence linear pair.

m∠4 , m∠2 are supplementary       r is a straight line hence linear pair.

Angle 2=180-62 = 118                      Definition of supplementary angles

Angle 4 = 180-118 =62                     -do-

Angle 1 = Angle 4                            Equality property

Step-by-step explanation:

Listed in the above answer!