Find the value of x and then the measure of Arc XYZ and Arc XZ. Show work on a piece of paper.

a) x =

b) Arc XYZ =

c) Arc XZ =

Given:

The measure of arc XY is (31x)°

The measure of arc YZ is (35x - 16)°

We need to determine the value of x, measure of arc XYZ and arc XZ.

Value of x:

From the figure, it is obvious that the arcs XY and YZ are congruent.

Thus, we have;

Subtracting both sides by 35x, we have;

Thus, the value of x is 4.

Measure of arc XYZ:

The measure of arc XYZ is given by

The measure of arc XY is given by

The measure of arc YZ is given by

Hence, the measure of arc XYZ is given by

Therefore, the measure of arc XYZ is 248°

Measure of arc XZ:

The measure of arc XZ is given by

Substituting the values, we have;

Thus, the measure of arc XZ is 112°