Exercise 14 Page 548

We know the measures of two angles. The measure of ∠ YXZ is 35^(∘) and the measure of ∠ WXV is 40^(∘). We want to find the measure of ∠ ZXW. Let x be the measure of this angle.

Because the angles in the diagram make up a straight line, we know that they are supplementary. This means that the sum of their measures is 180^(∘). We can create an equation using the expressions for the three smaller angles and their sum.

35 + x + 40 = 180

CommutativePropAdd

Commutative Property of Addition

x + 35 + 40 = 180

AddTerms

Add terms

x + 75 = 180

SubEqn

LHS-75=RHS-75

x + 75 - 75 = 180 - 75

SubTerms

Subtract terms

x = 105

We found that the measure of ∠ ZXW is 105^(∘). This corresponds to option B.