Question

what is the value of k?

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The angle \(54.4^{\circ}\) and \(k\) are not vertical angles. But \(k\) and the angle adjacent to \(54.4^{\circ}\) form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\).
Let \(k\) be the unknown angle. Then \(k + 54.4^{\circ}=180^{\circ}\).

Step2: Solve for \(k\)

Subtract \(54.4^{\circ}\) from both sides of the equation \(k + 54.4^{\circ}=180^{\circ}\).
\(k=180^{\circ}-54.4^{\circ}\)
\(k = 125.6^{\circ}\)

Answer:

\(125.6\)