Question

in the figure below, g || n. find the values of x and z.

Explanation:

Step1: Find the value of \( x \)

Since \( g \parallel n \) and the angle of \( 81^\circ \) and \( x^\circ \) are corresponding angles (or alternate interior angles, depending on the transversal), they are equal. So \( x = 81 \).

Step2: Find the value of \( z \)

We know that \( x \) and \( (3z - 24)^\circ \) are supplementary angles (they form a linear pair), so their sum is \( 180^\circ \).
We have \( x = 81 \), so substitute into the equation:
\( 81 + (3z - 24) = 180 \)
Simplify the left side: \( 81 - 24 + 3z = 180 \)
\( 57 + 3z = 180 \)
Subtract 57 from both sides: \( 3z = 180 - 57 \)
\( 3z = 123 \)
Divide both sides by 3: \( z = \frac{123}{3} = 41 \)

Answer:

\( x = 81 \), \( z = 41 \)