Find the value of each variable.

x = 143 degrees, y = 37 degrees and z = 143 degrees

Step-by-step explanation: First of all, looking at the line where x is situated,

37 + x = 180 {Sum of angles on a straight line equals 180}

Subtract 37 from both sides of the equation

x = 143

Next, looking at the line where y is situated, we observe that angle y is opposite of angle 37. Opposite angles are equal, therefore

y = 37

Alternatively, since angles x and y lie on the same line, and x has been calculated as 143, then

y + x = 180

y + 143 = 180

Subtract 143 from both sides of the equation

y = 37

Also looking at the line where angle z is situated, angle z is opposite angle x. Opposite angles are equal. Therefore z = 143.

Alternatively angle z and angle 37 lie on the same line. Therefore,

z + 37 = 180

Subtract 37 from both sides of the equation

z = 143

So all three variables are

x = 143, y = 37 and z = 143