Analyze the diagram below and complete the instructions that follow.Find the value of x and the value of y.A.x = 15, y = 10B.x = 20, y = 50C.x = 50, y = 10D.x = 50, y = 20Answer is C x=50 y=10

Answer:C. [tex]x=50[/tex], [tex]y=10[/tex]Step-by-step explanation:We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.We know that when two line intersect each other, then vertical angles are congruent.Using vertical angles theorem, we will get a system of equations as sown below:[tex]3y=x-20...(1)[/tex][tex]5x-100=y+140...(2)[/tex]From equation (1), we will get:[tex]x=3y+20[/tex]Upon substituting this value in equation (2), we will get:[tex]5(3y+20)-100=y+140[/tex][tex]5*3y+5*20-100=y+140[/tex][tex]15y+100-100=y+140[/tex][tex]15y=y+140[/tex][tex]15y-y=y-y+140[/tex][tex]14y=140[/tex][tex]\frac{14y}{14}=\frac{140}{14}[/tex][tex]y=10[/tex]Therefore, the value of y is 10.To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:[tex]3*10=x-20[/tex][tex]30=x-20[/tex][tex]30+20=x-20+20[/tex][tex]50=x[/tex]Therefore, the value of x is 50 and option C is the correct choice.