Question

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 =

Answer 1

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;

`31x=35x-16`

Subtracting both sides by 35x, we have;

`-4x=-16`

`x=4`

Thus, the value of x is 4.

Measure of arc XYZ:

The measure of arc XYZ is given by

`m \widehat{XYZ}=m \widehat{XY}+m \widehat{YZ}`

The measure of arc XY is given by

`m \widehat{X Y}=31(4)=124^(\circ)`

The measure of arc YZ is given by

`m \widehat{Y Z}=35(4)-16=124^(\circ)`

Hence, the measure of arc XYZ is given by

`m \widehat{XYZ}=124^(\circ)+124^(\circ)=248^(\circ)`

Therefore, the measure of arc XYZ is 248°

Measure of arc XZ:

The measure of arc XZ is given by

`m \widehat{XZ}=360^(\circ)-m \widehat{XYZ}`

Substituting the values, we have;

`m \widehat{XZ}=360^(\circ)-248^(\circ)`

`m \widehat{XZ}=112^(\circ)`

Thus, the measure of arc XZ is 112°