Question

Find the measure of each labeled angle as well as the values of x, y, and z.

Answer 1

Notice that the angle labelled as 3y and the angle with a measure of 72° are supplementary angles. Then:

$3y+72=180$

Substract 72 from both sides of the equation:

$\begin{gathered} 3y+72-72=180-72 \\ \Rightarrow3y=108 \end{gathered}$

The angle labelled as x and the angle labelled as 3y are corresponding angles. Then, they have the same measure:

$x=3y$

Since 3y=108, then:

$x=108$

On the equation 3y=108, divide both sides by 3 to find the value of y:

$\begin{gathered} \frac{3y}{3}=\frac{108}{3} \\ \Rightarrow y=36 \end{gathered}$

Finally, notice that the angle labelled as 3z+18 and the angle labelled as x are corresponding angles. Then, they have the same measure:

$3z+18=x$

Substitute x=108 and isolate z to find its value:

$\begin{gathered} \Rightarrow3z+18=108 \\ \Rightarrow3z=108-18 \\ \Rightarrow3z=90 \\ \Rightarrow z=\frac{90}{3} \\ \Rightarrow z=30 \end{gathered}$

Therefore, the measure of the angles labelled as 3z+18, x and 3y is 108°. The values of x, y and z are:

$\begin{gathered} x=108 \\ y=36 \\ z=30 \end{gathered}$