Question

in the figure below, ( k parallel l ) and ( m parallel n ). find the values of ( y ) and ( z ).

Explanation:

Step1: Find the value of \( z \)

Since \( k \parallel l \) and \( m \parallel n \), the angle \( (5z - 31)^\circ \) and \( 79^\circ \) are corresponding angles (or alternate interior angles, depending on the transversal), so they are equal.
Set up the equation: \( 5z - 31 = 79 \)
Add 31 to both sides: \( 5z = 79 + 31 \)
\( 5z = 110 \)
Divide both sides by 5: \( z = \frac{110}{5} = 22 \)

Step2: Find the value of \( y \)

The angle \( y^\circ \) and the angle \( (5z - 31)^\circ \) are corresponding angles (or vertical angles, or alternate interior angles, depending on the lines), so they are equal. We already found \( 5z - 31 = 79 \), so \( y = 79 \) (or we can substitute \( z = 22 \) into \( 5z - 31 \): \( 5\times22 - 31 = 110 - 31 = 79 \), so \( y = 79 \))

Answer:

\( y = 79 \), \( z = 22 \)