Question

what is the measure of angle a in the triangle shown? degrees

Explanation:

Step1: Recall the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle A=x\), \(\angle B = 54^{\circ}\), and \(\angle C=82^{\circ}\).

Step2: Apply the angle - sum formula

We use the formula \(x+\angle B+\angle C = 180^{\circ}\). Substitute \(\angle B = 54^{\circ}\) and \(\angle C = 82^{\circ}\) into the formula: \(x+54^{\circ}+82^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, simplify the left - hand side: \(x+(54 + 82)^{\circ}=x + 136^{\circ}\). Then, solve the equation \(x+136^{\circ}=180^{\circ}\) for \(x\). Subtract \(136^{\circ}\) from both sides: \(x=180^{\circ}-136^{\circ}\).

Answer:

\(44\)