Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

How do you calculate the angle measurement for the extended side of a triangle?

1. 180 minus the missing angle

2. Sum of all angles

3. Multiply the angle by the ratio

4. Subtract the angle from 90

The correct answer is: 180 minus the missing angle

To determine the angle measurement for the extended side of a triangle, one needs to understand the properties of angles within triangles. In any triangle, the sum of the interior angles is always 180 degrees. When discussing an extended side, we are often referring to the exterior angle formed by extending one side of the triangle. The exterior angle at any vertex of a triangle is equal to the sum of the two non-adjacent interior angles. If you have one of the interior angles and want to find the exterior angle at that vertex, you can calculate it by subtracting the measure of the interior angle from 180 degrees. This is because the straight line at the vertex along with the interior angle forms a straight angle, which measures 180 degrees. Thus, if you're looking for the measurement of the angle for the extended side, you would subtract the measure of the interior angle from 180 degrees, which aligns perfectly with the correct answer. This understanding is crucial in geometry when analyzing angles related to triangles and their extensions.