Question

if triangle abc is a right - triangle and m∠a = 40°, what are possible measures for angles b and c?

angle	measure (degrees)

|∠b|
|∠c|

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°. Given \(m\angle A = 40^{\circ}\).

Step2: Case 1: \(\angle A\) is not the right - angle

Let \(\angle C=90^{\circ}\). Then, using the angle - sum property \(m\angle A + m\angle B+m\angle C = 180^{\circ}\). Substitute \(m\angle A = 40^{\circ}\) and \(m\angle C = 90^{\circ}\) into the equation: \(40^{\circ}+m\angle B + 90^{\circ}=180^{\circ}\). Solve for \(m\angle B\): \(m\angle B=180^{\circ}-(40^{\circ} + 90^{\circ})=50^{\circ}\).

Step3: Case 2: \(\angle A\) is the right - angle (not possible as \(m\angle A = 40^{\circ}

eq90^{\circ}\))

Answer:

Angle	Measure (degrees)
\(\angle B\)	50
\(\angle C\)	90