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 \( 119-y=180 \)

To solve for \( x \) and \( y \), we need to recognize the relationships between the angles in the diagram. Typically, angles in geometric figures either add up to 180 degrees (as in a triangle) or they can be complementary (adding up to 90 degrees). Moving on to our equations, based on the structure given: 1. The equation for angle \( x \) can be derived assuming angles fit the triangle sum of 180 degrees: \( 37 + x + 35 = 180 \). 2. For the measurement of \( y \), since we've \( \mathrm{m} \angle 1 = (119 - y)^9 \) and we need this to be an angle relevant for complementary conditions, it would be logical to consider \( 119 - y = 90 \). Now putting these together, we can review the options: By analyzing: 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 correct option that fits our derived relationships is **B**: \( 37 + x + 35 = 180 \) and \( 119 - y = 90 \). Once we've chosen option B: 1. For \( x \), rearranging gives \( x = 180 - 37 - 35 = 108 \). 2. For \( y \), we find \( y = 119 - 90 = 29 \). Thus, \( x = 108 \) and \( y = 29 \). Happy calculating!