Let's look at the relevant parts of the diagram. We are given the measure of one of the angles formed by two intersecting lines, and we are asked to find the measure of an adjacent angle. Let's call the given angle ∠ 8. The information on the diagram tells us that m ∠ 8=53^(∘).
From the diagram, we can see that ∠ 8 and ∠ 6 form a linear pair.
According to the Supplement Theorem, angles in a linear pair are supplementary. By the definition of supplementary angles, this means, that the sum of their measures is 180^(∘).
m ∠ 8+m ∠ 6=180^(∘)
It is given that m ∠ 8=53^(∘), so according to the Substitution Property of Equality, we can replace m ∠ 8 with 53^(∘).
53^(∘)+m ∠ 6=180^(∘)
According to the Subtraction Property of Equality, we can subtract 53^(∘) from both sides of the equation.
m ∠ 6=127^(∘)
Thus, we proved that the measure of ∠ 6 is 127^(∘).
