Question

in the figure below, m || n and p || q. find the values of y and x.

Explanation:

Step1: Find y using corresponding angles

Since \( p \parallel q \) and \( m \) is a transversal, the \( 67^\circ \) angle and \( y^\circ \) are corresponding angles. Corresponding angles are equal when lines are parallel. So \( y = 67 \).

Step2: Find x using corresponding angles

Since \( m \parallel n \) and \( q \) is a transversal, the angle \( (5x - 43)^\circ \) and \( y^\circ \) are corresponding angles. So \( 5x - 43 = y \). We know \( y = 67 \), so substitute:
\( 5x - 43 = 67 \)
Add 43 to both sides:
\( 5x = 67 + 43 \)
\( 5x = 110 \)
Divide by 5:
\( x = \frac{110}{5} = 22 \)

Answer:

\( y = 67 \), \( x = 22 \)