Question

given the figure below, find the values of x and z.
(8x - 30)°
z°
(7x - 15)°
x =
z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(8x - 30=7x - 15\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(8x-7x - 30=7x-7x - 15\), which simplifies to \(x-30=-15\). Then add 30 to both sides: \(x=-15 + 30\), so \(x = 15\).

Step3: Find the measure of one of the vertical angles

Substitute \(x = 15\) into \(8x - 30\): \(8\times15-30=120 - 30=90^{\circ}\).

Step4: Use the linear - pair property to find \(z\)

The angle with measure \(z^{\circ}\) and the \(90^{\circ}\) angle are a linear - pair. So \(z+90 = 180\). Subtract 90 from both sides: \(z=180 - 90\), so \(z = 90\).

Answer:

\(x = 15\)
\(z = 90\)