Question

what is the value of r?

Explanation:

Step1: Identify angle - relationship

The angle adjacent to the 57 - degree angle and the angle \(r\) are vertical angles. Vertical angles are equal. First, find the angle adjacent to the 57 - degree angle. The sum of adjacent angles forming a straight - line is 180 degrees. Let the adjacent angle to 57 degrees be \(x\). So \(x + 57^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

\(x=180^{\circ}-57^{\circ}=123^{\circ}\).

Step3: Find \(r\)

Since \(r\) and \(x\) are vertical angles, \(r = x\). So \(r = 123^{\circ}\).

Answer:

\(123\)