Parts of a Right Triangle: Angles

Throughout this unit, we are going to be working with right triangles.  We need to be sure we know the names of each part, where each part is within the triangle, and the properties of each part of the triangle.

Let’s start with the angles.  As you know, a right triangle must have one and only one right angle.  This angle is often marked with a small square indicating that it is a right angle.  

Right triangle

The other two angles will be acute angles.

The sum of the angles in any triangle is 180°.  Let’s say that the two acute angles are A and B, and the right angle measures 90°.  We can use this information to write the equation:

A + B + 90 = 180 

Subtract 90 from both sides.

A + B = 90

This equation tells us that the two acute angles in a right triangle are complimentary.

Example:
If one of the acute angles in a right triangle measures 42°, what is the measure of the other acute angle?

Right triangle

Solution:
x + 42 = 90
x = 48

The other acute angle measures 48°.