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

Find The Measure Of Each Labeled Angle As Well As The Values Of X Y And Z class=

Sagot :

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

[tex]3y+72=180[/tex]

Substract 72 from both sides of the equation:

[tex]\begin{gathered} 3y+72-72=180-72 \\ \Rightarrow3y=108 \end{gathered}[/tex]

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

[tex]x=3y[/tex]

Since 3y=108, then:

[tex]x=108[/tex]

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

[tex]\begin{gathered} \frac{3y}{3}=\frac{108}{3} \\ \Rightarrow y=36 \end{gathered}[/tex]

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

[tex]3z+18=x[/tex]

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

[tex]\begin{gathered} \Rightarrow3z+18=108 \\ \Rightarrow3z=108-18 \\ \Rightarrow3z=90 \\ \Rightarrow z=\frac{90}{3} \\ \Rightarrow z=30 \end{gathered}[/tex]

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

[tex]\begin{gathered} x=108 \\ y=36 \\ z=30 \end{gathered}[/tex]

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