Question

1. janie created triangle abc with the given angle measures. part a: which equation could be written to solve for the unknown angle of triangle abc? a. 78° - 37°+∠b = 180° b. 78° + 37°=∠b c. 78° + 37°+180°=∠b d. 78°+∠b + 37°=180° part b: what is the measurement of ∠b?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle ABC\), if \(\angle A = 78^{\circ}\), \(\angle C=37^{\circ}\), and \(\angle B\) is the unknown angle, then \(\angle A+\angle B+\angle C = 180^{\circ}\).

Step2: Substitute the known angles into the equation

We know that \(78^{\circ}+\angle B + 37^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle B\)

First, simplify the left - hand side: \(78^{\circ}+37^{\circ}=115^{\circ}\), so the equation becomes \(115^{\circ}+\angle B=180^{\circ}\). Then, subtract \(115^{\circ}\) from both sides: \(\angle B=180^{\circ}-115^{\circ}=65^{\circ}\).

For Part A:
The correct equation based on the angle - sum property of a triangle is \(78^{\circ}+37^{\circ}+\angle B = 180^{\circ}\), so the answer is C.

For Part B:

Step1: Use the equation \(78^{\circ}+37^{\circ}+\angle B = 180^{\circ}\)

Combine like terms on the left - hand side: \(115^{\circ}+\angle B = 180^{\circ}\).

Step2: Isolate \(\angle B\)

Subtract \(115^{\circ}\) from both sides of the equation: \(\angle B=180^{\circ}-(78^{\circ} + 37^{\circ})=65^{\circ}\)

Answer:

Part A: C. \(78^{\circ}+37^{\circ}+\angle B = 180^{\circ}\)
Part B: \(65^{\circ}\)