Question

what is the value of k?
57.7°

Explanation:

Step1: Use the property of angles around a point

The sum of angles around a point is \(360^{\circ}\). But here, we can also note that the vertical angles and right - angle relationships. The sum of the given angle \(57.7^{\circ}\), the right - angle \(90^{\circ}\) and \(k\) is \(180^{\circ}\) (since they are adjacent angles on a straight line).

Step2: Set up the equation

\(k + 57.7^{\circ}+90^{\circ}=180^{\circ}\)

Step3: Solve for \(k\)

\(k=180^{\circ}-(57.7^{\circ} + 90^{\circ})\)
\(k=180^{\circ}-147.7^{\circ}\)
\(k = 32.3^{\circ}\)

Answer:

\(32.3\)