Question

problem set 1: triangle sum and exterior angle theorems determine the measure of the unknown angle in each triangle.

Explanation:

Step1: Recall triangle - sum theorem

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle ABC$, we know $\angle B = 90^{\circ}$ and $\angle C=40^{\circ}$, and we want to find $\angle A$. Let $\angle A=x$. Then $x + 90^{\circ}+40^{\circ}=180^{\circ}$.

Step2: Solve for the unknown angle

We can simplify the equation $x+90 + 40=180$ to $x+130 = 180$. Subtracting $130^{\circ}$ from both sides of the equation, we get $x=180^{\circ}-130^{\circ}$.

Answer:

$50^{\circ}$