Question

in \\( \triangle a b c , m \angle a = 4 3 ^ { \circ } \\) and \\( m \angle b = 1 5 ^ { \circ } \\). what is \\( m \angle c \\)?
\\( m \angle c = \\)

Explanation:

Step1: Recall the triangle - angle sum theorem

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

Step2: Substitute the given values of \(m\angle A\) and \(m\angle B\)

We know that \(m\angle A = 42^{\circ}\) and \(m\angle B = 85^{\circ}\). Substituting into the formula: \(42^{\circ}+85^{\circ}+m\angle C = 180^{\circ}\).

Step3: Solve for \(m\angle C\)

First, calculate \(42 + 85=127\). Then, \(m\angle C=180^{\circ}-(42^{\circ}+85^{\circ})=180 - 127\).

Answer:

\(53\)