Question

1. connecting the 3 bases in a baseball field creates a right triangle. if the interior angle at 3rd base is 40 degrees, what is the measure of the exterior angle that 2nd base makes with the foul line?

Explanation:

Step1: Find the interior angle at 2nd base

In a right - triangle (right angle at 1st base, assume), sum of interior angles of a triangle is \(180^{\circ}\). Let the interior angle at 2nd base be \(x\). We know one angle is \(90^{\circ}\) (right - triangle) and another is \(40^{\circ}\). Using the formula \(x+90^{\circ}+40^{\circ}=180^{\circ}\), we can solve for \(x\).

$$x = 180^{\circ}-(90^{\circ}+40^{\circ})=50^{\circ}$$

Step2: Find the exterior angle at 2nd base

The exterior angle and the interior angle at a vertex are supplementary (sum to \(180^{\circ}\)). Let the exterior angle be \(y\). If the interior angle \(x = 50^{\circ}\), then \(y+x=180^{\circ}\).

$$y=180^{\circ}-x$$

Substitute \(x = 50^{\circ}\) into the formula:

$$y=180^{\circ}-50^{\circ}=130^{\circ}$$

Answer:

\(130^{\circ}\)