Question

in triangle abc, the measure of angle b is 33° and the measure of angle c is 24°. what is the measure of angle a?
a 9°
b 33°
c 57°
d 123°

Explanation:

Step1: Recall the sum of angles in a triangle

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

Step2: Substitute the known values

We know that \(\angle B = 33^{\circ}\) and \(\angle C=24^{\circ}\). Substituting these into the equation \(\angle A+\angle B+\angle C = 180^{\circ}\), we get \(\angle A+33^{\circ}+24^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle A\)

First, simplify the left - hand side: \(33^{\circ}+24^{\circ}=57^{\circ}\). Then the equation becomes \(\angle A + 57^{\circ}=180^{\circ}\). Subtract \(57^{\circ}\) from both sides: \(\angle A=180^{\circ}-57^{\circ}\).

Answer:

\(123^{\circ}\) (Option D)