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

Work Shown:

The left and right angles (119 and 9x+83) are vertical angles.

Therefore, they are congruent or equal angles.

9x+83 = 119

9x = 119-83 subtract 83 from both sides

9x = 36

x = 36/9 divide both sides by 9

x = 4

To find the value of z, we take advantage of the fact that angles 119 and z are supplementary. They add to 180 degrees.

z+119 = 180

z = 180-119 subtract 119 from both sides

z = 61

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.