Question

find the measure of angle c.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, in \(\triangle ABC\), \(\angle A+\angle B+\angle C = 180^{\circ}\).

Step2: Substitute the given angle values

We know that \(\angle A = 67^{\circ}\) and \(\angle B=46^{\circ}\). Substituting these values into the angle - sum formula gives \(67^{\circ}+46^{\circ}+\angle C=180^{\circ}\).

Step3: Solve for \(\angle C\)

First, add the known angles: \(67 + 46=113\). Then, we have \(113^{\circ}+\angle C = 180^{\circ}\). Subtracting 113° from both sides gives \(\angle C=180^{\circ}- 113^{\circ}=67^{\circ}\).

Answer:

\(67^{\circ}\)