Question

given \\( \delta abc \\), what is \\( m \angle c \\)?
\\( m \angle c = ? ^ { \circ } \\)

Explanation:

Step1: Recall the triangle - angle sum theorem

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

Step2: Substitute the known values

We know that \(m\angle A = 80^{\circ}\) and \(m\angle B = 55^{\circ}\). Substituting these into the formula: \(80^{\circ}+55^{\circ}+m\angle C=180^{\circ}\).

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

First, simplify the left - hand side: \(135^{\circ}+m\angle C=180^{\circ}\). Then, subtract \(135^{\circ}\) from both sides: \(m\angle C=180^{\circ}- 135^{\circ}\).

Answer:

\(45\)