Question

given (\triangle abc), what is (mangle c)? (mangle c = ?^{circ})

Explanation:

Step1: Recall the triangle angle - sum theorem

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

Step2: Substitute the known angles

We know that \(m\angle A = 95^{\circ}\) and \(m\angle B = 30^{\circ}\). Substituting these values into the equation \(m\angle A + m\angle B+m\angle C=180^{\circ}\), we get \(95^{\circ}+30^{\circ}+m\angle C = 180^{\circ}\).

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

First, simplify the left - hand side of the equation: \(95 + 30+m\angle C=180\), which is \(125+m\angle C=180\). Then, subtract \(125\) from both sides: \(m\angle C=180 - 125\).

Answer:

\(55\)