Question

what is the value of r?

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The sum of \(r + 80^{\circ}\) is equal to the sum of the other pair of vertical angles.

Step2: Set up the equation

Since \(r+80^{\circ}\) and \(38^{\circ}+80^{\circ}\) are vertical angles (by the property of vertical angles in geometry), we have \(r + 80^{\circ}=38^{\circ}+80^{\circ}\).
Subtract \(80^{\circ}\) from both sides of the equation: \(r=38^{\circ}\)

Answer:

\(38^{\circ}\)