Question

given δabc, what is m∠c?
65°
55°
m∠c = ?°

Explanation:

Step1: Recall the triangle - angle sum theorem

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

Step2: Substitute the known values

We know that \(m\angle A = 65^{\circ}\) and \(m\angle B = 55^{\circ}\). Substituting these into the equation \(65^{\circ}+55^{\circ}+m\angle C = 180^{\circ}\).

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

First, calculate \(65 + 55=120\). Then the equation becomes \(120^{\circ}+m\angle C=180^{\circ}\). Subtract \(120^{\circ}\) from both sides: \(m\angle C=180^{\circ}- 120^{\circ}\).

Answer:

\(60\)