Question

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°

Answer 1

Given

m∠1 = 62°

lines t and l intersect

Prove: m∠4 = 62°

To proof

Angle addition property

Two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

As shown in the diagram

m ∠1 + m∠ 2 = 180 °

( by linear pair property )

Given:

m∠1 = 62°

Put in the above equation

we get

m∠ 2 = 180° -62°

m ∠2= 118°

Also

m∠ 2 + m∠4 = 180°

( By linear pair property )

m∠4 = 180° - 118°

m ∠4 = 62°

Hence proved