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 sum of angles in a linear - pair is \(180^{\circ}\). So, \(z+89 = 180\).

Step4: Solve for \(z\)

Subtract 89 from both sides of the equation \(z+89 = 180\), \(z=180 - 89\), \(z = 91\).

Answer:

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