Question

what is the value of k?

Explanation:

Step1: Recall angle - sum property

The sum of the angles in the given figure is 180°. So, \(k + 28.2^{\circ}+78.2^{\circ}=180^{\circ}\).

Step2: Solve for \(k\)

First, simplify the left - hand side: \(k+(28.2 + 78.2)^{\circ}=180^{\circ}\), which gives \(k + 106.4^{\circ}=180^{\circ}\). Then, subtract \(106.4^{\circ}\) from both sides: \(k=180^{\circ}-106.4^{\circ}\). So, \(k = 73.6^{\circ}\).

Answer:

\(73.6\)