Question

given the figure below, find the values of x and z.

Explanation:

Step1: Find x using vertical angles

Vertical angles are equal, so \(8x - 42 = 62\).
Add 42 to both sides: \(8x = 62 + 42 = 104\).
Divide by 8: \(x = \frac{104}{8} = 13\).

Step2: Find z using linear pair

A linear pair of angles sums to \(180^\circ\), so \(z + 62 = 180\).
Subtract 62: \(z = 180 - 62 = 118\).

Answer:

\(x = 13\), \(z = 118\)