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 angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In a right - triangle, one angle is $90^{\circ}$.

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

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

Step3: Case 2: $\angle A$ is the right - angle

This is not possible since $m\angle A = 40^{\circ}
eq90^{\circ}$.

Answer:

$\angle B = 50^{\circ}$, $\angle C = 90^{\circ}$