Question

1. using the picture, find the following: m∠a = select m∠b = 90°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In right - triangle ABC, we know that \(m\angle B = 90^{\circ}\) and \(m\angle C=64^{\circ}\). Let \(m\angle A=x\). Then \(x + m\angle B+m\angle C = 180^{\circ}\).

Step2: Substitute the known values

Substitute \(m\angle B = 90^{\circ}\) and \(m\angle C = 64^{\circ}\) into the equation \(x + m\angle B+m\angle C=180^{\circ}\). We get \(x+90^{\circ}+64^{\circ}=180^{\circ}\).

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

First, simplify the left - hand side of the equation: \(x+(90^{\circ}+64^{\circ})=x + 154^{\circ}\). Then, solve for \(x\): \(x=180^{\circ}-154^{\circ}\). So \(x = 26^{\circ}\), which means \(m\angle A=26^{\circ}\).

Answer:

\(m\angle A = 26^{\circ}\)