By Trisha Dawe – Updated Aug 30, 2022

Every triangle—whether right, isosceles, acute, obtuse, equilateral, or scalene—conforms to one simple truth: the sum of its interior angles is always 180°.

Using the defining characteristics of each triangle type, you can determine any missing angle with ease. The following sections walk you through three common scenarios.

Calculating Angles When Two Are Known

Step 1 – Draw and Label

Sketch the triangle (if no diagram is provided) and label the two known angles with their measured degrees.

Step 2 – Add the Known Angles

Sum the two angles. Example:

Angle A = 30°
Angle B = 45°
30° + 45° = 75°

Step 3 – Compute the Third Angle

Subtract the sum from 180° to find the third angle.

180° – 75° = 105°
Angle C = 105°

Step 4 – Verify

Confirm that all three angles add to 180°.

30° + 45° + 105° = 180°

Calculating Angles When Only One Is Known

Step 1 – Identify the Triangle Type

For one‑known‑angle problems, common triangle types are isosceles or right. Label the known angle and set up an equation based on the triangle’s properties.

Step 2 – Set Up the Equation

Isosceles Example:

Angle A = x°
Angle B = x°
Angle C = 80°
x + x + 80° = 180°

Right‑triangle Example:

Angle A = 90°
Angle B = 15°
Angle C = x°
90° + 15° + x° = 180°

Step 3 – Solve for x

Isosceles:
2x = 100°
x = 50°

Right triangle:
105° + x° = 180°
x = 75°

Step 4 – Verify

Check the sum of all angles.

Isosceles: 50° + 50° + 80° = 180°
Right triangle: 90° + 15° + 75° = 180°

Calculating Angles When None Are Known (Equilateral Triangle)

Step 1 – Sketch the Triangle

Draw an equilateral triangle and denote each angle with an unknown variable x, since all three angles are equal.

Step 2 – Form the Equation

x + x + x = 180°

Step 3 – Solve for x

3x = 180°
x = 60°

Step 4 – Verify

60° + 60° + 60° = 180°

By following these straightforward steps, you can accurately determine any missing angle in any triangle type.