Question

find the values of v, w, x, and y.

Explanation:

Step1: Find \( w \)

Use the triangle - angle sum theorem (\( 180^{\circ}\) in a triangle).
\( w = 180-(42 + 87)\)
\( w=180 - 129\)
\( w = 51\)

Step2: Find \( x \)

Vertical angles are equal. The angle opposite to \( 87^{\circ}\) is also \( 87^{\circ}\). Using the triangle - angle sum theorem for the left - hand triangle.
\( x=180-(42 + 51)\)
\( x = 87\)

Step3: Find \( y \)

Alternate - interior angles (parallel lines cut by a transversal).
\( y = 20\)

Step4: Find \( v \)

Using the triangle - angle sum theorem for the right - hand triangle.
\( v=180-(87 + 20)\)
\( v=73\)

Answer:

\( v = 73\), \( w = 51\), \( x = 87\), \( y = 20\)