Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

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

Step2: Substitute the known angle measures

We know that \(m\angle B = 45^{\circ}\) and \(m\angle C=60^{\circ}\). Then the equation becomes \(m\angle A+45^{\circ}+60^{\circ}=180^{\circ}\).

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

First, simplify the left - hand side: \(m\angle A+(45 + 60)^{\circ}=m\angle A + 105^{\circ}\). Then, using the subtraction property of equality, \(m\angle A=180^{\circ}-105^{\circ}\).

Answer:

\(75\)