If a triangle has angles measuring 60 degrees and 90 degrees, what is the measure of the third angle?

In any triangle, the sum of the interior angles is always 180 degrees. In this case, two angles are given: one measuring 60 degrees and the other measuring 90 degrees. To find the measure of the third angle, you can add the measures of the two known angles together and then subtract that sum from 180 degrees.

So, first sum the known angles:

60 degrees + 90 degrees = 150 degrees.

Next, subtract this sum from 180 degrees to find the measure of the third angle:

180 degrees - 150 degrees = 30 degrees.

Therefore, the measure of the third angle is 30 degrees. This process illustrates how to use the properties of triangles to determine unknown angle measures based on the known sums of angles in a triangle.