Question

Write a two-column proof for the following:

Given: Angle 1 and Angle 2 form a linear pair, and the measure of Angle 1 is twice the measure of Angle 2.
Prove: The measure of Angle 2 = 60

Answer 1

Starting with the given information, we used the definition of a linear pair and properties of equation solving to prove that the measure of Angle 2 is 60 degrees.

Step-by-step explanation:

We are given that Angle 1 and Angle 2 form a linear pair, and that the measure of Angle 1 is twice the measure of Angle 2. By definition, a linear pair of angles are adjacent angles whose non-common sides are opposite rays. This means that the sum of the measures of Angle 1 and Angle 2 is 180 degrees since they form a straight line.

Let's denote the measure of Angle 1 as m∠1 and the measure of Angle 2 as m∠2. The problem states m∠1 = 2m∠2. Since we know that m∠1 + m∠2 = 180° (the sum of angles in a linear pair is 180 degrees), we can substitute 2m∠2 in place of m∠1 which gives us 2m∠2 + m∠2 = 180°.

Solving for m∠2 in the equation 2m∠2 + m∠2 = 180°, we combine like terms to get 3m∠2 = 180°, and then divide both sides by 3 to find that m∠2 = 60°.

We have now proven that the measure of Angle 2 is 60 degrees.