Question

in the image below, new path and east path are parallel. find the measure of:

Explanation:

Step1: Find \( y \)

Vertical angles are equal. So \( y = 47^{\circ} \)

Step2: Find \( z \)

In a triangle, the sum of angles is \( 180^{\circ} \). So \( z=180^{\circ}-47^{\circ}-72^{\circ}=61^{\circ} \)

Step3: Find \( w \)

Alternate - interior angles (since New Path and East Path are parallel). So \( w = 72^{\circ} \)

Step4: Find \( x \)

Alternate - interior angles (since New Path and East Path are parallel). So \( x = 61^{\circ} \)

Answer:

\( x = 61^{\circ}, y = 47^{\circ}, z = 61^{\circ}, w = 72^{\circ} \)