Question

given the figure below, find the values of x and z.
(10x - 51)°
89°
z°
x=
z=

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(10x - 51=89\).

Step2: Solve for \(x\)

Add 51 to both sides of the equation \(10x - 51=89\): \(10x=89 + 51\), \(10x=140\). Then divide both sides by 10, \(x = 14\).

Step3: Use linear - pair property

The angles \((10x - 51)^{\circ}\) and \(z^{\circ}\) form a linear - pair, so \((10x - 51)+z = 180\). Since \(10x-51 = 89\), then \(89+z=180\). Subtract 89 from both sides: \(z=180 - 89\), \(z = 91\).

Answer:

\(x = 14\)
\(z = 91\)