Question

in the figure below, n || l.
find the values of x and z.
x =
z =
(3z + 51)°
60°

Explanation:

Step1: Determine x using supplementary angles

Since \( n \parallel l \) and the transversal \( q \) creates a \( 60^\circ \) angle and \( x^\circ \), they are supplementary (linear pair). So \( x + 60 = 180 \).
\( x = 180 - 60 = 120 \)

Step2: Determine z using corresponding angles

The angle \( (3z + 51)^\circ \) and \( x^\circ \) are corresponding angles (since \( n \parallel l \)), so \( 3z + 51 = x \). We know \( x = 120 \), so:
\( 3z + 51 = 120 \)
\( 3z = 120 - 51 = 69 \)
\( z = \frac{69}{3} = 23 \)

Answer:

\( x = 120 \), \( z = 23 \)