Final answer:
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.