Question

3-2 algebra and parallel lines and transversals pract find the value of each variable in the figure below. (8x - 10)° (6y + 20)° (7x)° z° ****just type the number and nothing else. x = y = z =

Explanation:

Step1: Use corresponding - angles property

Since the two lines are parallel, the corresponding angles are equal. So, \(8x - 10=7x\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides of the equation \(8x - 10 = 7x\). We get \(8x-7x=10\), so \(x = 10\).

Step3: Use linear - pair property

The angle \((6y + 20)^{\circ}\) and \((7x)^{\circ}\) form a linear - pair. Since \(x = 10\), then \((7x)^{\circ}=70^{\circ}\). And \(6y+20 + 70=180\) (because the sum of angles in a linear - pair is \(180^{\circ}\)).

Step4: Solve for \(y\)

First, simplify the equation \(6y+20 + 70=180\) to \(6y+90 = 180\). Then subtract 90 from both sides: \(6y=180 - 90=90\). Divide both sides by 6: \(y=\frac{90}{6}=15\).

Step5: Use vertical - angles property

The angle \(z^{\circ}\) and \((6y + 20)^{\circ}\) are vertical angles. Substitute \(y = 15\) into \(6y + 20\), we get \(6\times15+20=90 + 20=110\). So \(z = 110\).

Answer:

\(x = 10\)
\(y = 15\)
\(z = 110\)