Question

given \\( \triangle abc \\), what is \\( m\angle b \\)?

\\( m\angle b = ? ^ { \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 \(m\angle A = 80^{\circ}\) and \(m\angle C=70^{\circ}\). Substituting these values into the equation \(m\angle A + m\angle B+m\angle C=180^{\circ}\), we get \(80^{\circ}+m\angle B + 70^{\circ}=180^{\circ}\).

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

First, simplify the left - hand side of the equation: \(80 + 70+m\angle B=180\), which is \(150^{\circ}+m\angle B=180^{\circ}\). Then, subtract \(150^{\circ}\) from both sides: \(m\angle B=180^{\circ}-150^{\circ}\).

Answer:

\(30\)