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<u>Given</u>:
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.
<u>Value of x:</u>
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.
<u>Measure of arc XYZ:</u>
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°
<u>Measure of arc XZ:</u>
The measure of arc XZ is given by
Substituting the values, we have;
Thus, the measure of arc XZ is 112°