Given the figure below, find the values of x and z

62 and 11x - 37 are vertical angles, and so they are the same measurements, and will equal each other

11x - 37 = 62

Isolate the x. Do the opposite of PEMDAS. Note the equal sign, what you do to one side you do to the other.

Add 37 to both sides:

11x - 37 (+37) = 62 (+37)

11x = 62 + 37

11x = 99

Isolate the x. Divide 11 from both sides

11x/11 = 99/11

x = 99/11

m∠x = 9°

To solve for z, use the supplementary angle.

A supplementary angle = 180°

Add z with 62, and place it equal to 180

180 = z + 62

Isolate the variable. Subtract 62 from both sides

180 (-62) = z + 62 (-62)

z = 180 - 62

m∠z = 118°

hope this helps

Remark

x should be solved first.

The Left and Right angles are vertically opposite and equal. Intersecting lines have that property.

11x - 37 = 62 Equate

11x - 37 + 37 = 62 + 37 Add

11x = 99

x = 99/11 Divide by 11

x = 9

11*9 - 37 = 62

99 - 37 = 62

Z and 62 are on the same straight line. They are supplementary which means they add to 180o (That's the definition of supplementary.

z + 62 = 180 Subtract 62

z = 180 - 62

z = 118