Find a Missing Right-Triangle Angle

Find a Missing Right-Triangle Angle

A right triangle always has one angle of 90°. Since the angles in any triangle add to 180°, the two acute angles must add to 90°. That is the key fact for these problems.

Method

1. Identify the right angle. Mark the 90° angle first.

2. Use the angle sum. Add the known angles.

3. Subtract from 180° if you are finding the third angle:

   [ \text{missing angle} = 180^\circ - (90^\circ + \text{known angle}) ]

4. Simplify the result and write the answer in degrees.

If two angles are given

If both acute angles are known, you can also use:

[ \text{acute angle}_1 + \text{acute angle}_2 = 90^\circ ]

So the missing acute angle is:

[ 90^\circ - \text{known acute angle} ]

Check your answer

• The angle must be less than 90° if it is an acute angle.
• All three angles should add to 180°.
• If you found the other acute angle, it should complement the known one to 90°.

This process works every time because every right triangle has exactly one right angle and two complementary acute angles.