Question

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

Explanation:

Step1: Use the property of parallel lines and transversal (corresponding angles)

Since \(m\parallel n\) and \(p\parallel q\), \(x = 67^{\circ}\) (corresponding angles).

Step2: Use the property of parallel lines and transversal (alternate interior angles)

\(4y- 13=67\) (alternate interior angles).
Solve the equation \(4y-13 = 67\):
Add \(13\) to both sides: \(4y=67 + 13\), so \(4y=80\).
Divide both sides by \(4\): \(y=\frac{80}{4}=20\).

Answer:

\(x = 67\), \(y = 20\)