Question

in \\( \triangle abc \\), the measure of \\( \angle a \\) is \\( 40 ^ { \circ } \\) and the measure of \\( \angle b \\) is \\( 65 ^ { \circ } \\). what is the measure of \\( \angle c \\)?

Explanation:

Step1: Recall the sum of angles in a triangle

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

Step2: Substitute the given values

We know \(\angle A = 40^{\circ}\) and \(\angle B=65^{\circ}\). Substituting into the formula: \(40^{\circ}+65^{\circ}+\angle C = 180^{\circ}\).

Step3: Solve for \(\angle C\)

First, calculate \(40 + 65=105\). Then, \(\angle C=180^{\circ}-105^{\circ}\).

Answer:

\(\angle C = 75^{\circ}\), so the answer is D. \(75^{\circ}\)