If two of the angles in a right triangle measure 30 degrees and 60 degrees, what is the measure of the third angle?

In a triangle, the sum of all three angles must equal 180 degrees. In a right triangle, one of the angles is always 90 degrees. Therefore, if two angles measure 30 degrees and 60 degrees, you can find the measure of the third angle by applying the rule of angle sums.

First, add the two known angles: 30 degrees + 60 degrees = 90 degrees. Since the total angle sum for any triangle is 180 degrees, to find the third angle, you can subtract the sum of the known angles from 180 degrees.

So, 180 degrees - 90 degrees equals 90 degrees. This indicates that the measure of the third angle in this right triangle is indeed 90 degrees, which fits perfectly within the definition of a right triangle, where one angle is always 90 degrees.

Thus, identifying the third angle as 90 degrees confirms the fundamental properties of triangle geometry, specifically regarding right triangles.