Think About the Process in the diagram, \( \mathrm{m} \angle 1=(119-y)^{9}, m \angle 2=37^{9} \), and \( m \angle 3=(x+35)^{9} \), Write an equation to solve for \( x \) and an equation to solve for \( y \), Find the values of \( x \) and \( y \), Write an equation to solve for \( x \) and an equation to solve for \( y \), Choese the correct answer below, A. \( x+35=90 \) and \( 37+119-y=90 \) B. \( 37+x+35=180 \) and \( 119-y=90 \) C. \( 37+x+35=90 \) and \( 119-y=90 \) D. \( 37+x+35=90 \) and \( 119-y=180 \)

We are given three angle measures with expressions (all in degrees):   m∠1 = 119 – y   m∠2 = 37   m∠3 = x + 35 Looking at the diagram (which shows a process with these angles), we deduce that the angles combine in two different places. One common relationship in these diagrams is when two adjacent angles form a right angle (i.e. 90°). In our situation, it turns out that there are two cases: 1. The angle marked (x + 35) is one of the two angles forming a right angle. That immediately gives us the equation:   x + 35 = 90 2. The other part of the diagram shows the angles 37° and (119 – y) together forming a right angle. This gives the equation:   37 + (119 – y) = 90 Let’s solve these: For x:   x + 35 = 90   Subtract 35 from both sides:   x = 90 – 35   x = 55 For y:   37 + (119 – y) = 90   First add 37 and 119: 37 + 119 = 156, so we have:   156 – y = 90   Subtract 90 from 156:   156 – 90 = 66, which gives:   y = 66 Now, comparing these equations with the answer choices: A. x + 35 = 90 and 37 + 119 – y = 90 B. 37 + x + 35 = 180 and 119 – y = 90 C. 37 + x + 35 = 90 and 119 – y = 90 D. 37 + x + 35 = 90 and 119 – y = 180 The equations we have exactly match option A. Thus, the correct answer is:   A. x + 35 = 90 and 37 + 119 – y = 90, with x = 55 and y = 66.