Question

what is the measure of k? 36° 74°

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Set up the equation

Let the exterior angle be \(36^{\circ}\), and the two non - adjacent interior angles be \(k\) and \(74^{\circ}\). So, \(36^{\circ}=k + 74^{\circ}\) is incorrect. It should be that if we consider the correct exterior - angle relationship, assume the exterior angle adjacent to the angle we want to find. The exterior angle of the triangle at the vertex with angle \(k\) is \(180^{\circ}-k\). And using the exterior - angle property, \(180^{\circ}-k=74^{\circ}+36^{\circ}\).

Step3: Solve for \(k\)

First, simplify the right - hand side: \(74^{\circ}+36^{\circ}=110^{\circ}\). Then we have \(180^{\circ}-k = 110^{\circ}\). Rearranging the equation to solve for \(k\), we get \(k=180^{\circ}-110^{\circ}\).
\(k = 70^{\circ}\)

Answer:

\(70^{\circ}\)