The Lesson

To find the missing angle of a triangle, use the fact that the interior angles of a triangle add up to 180°.

If any of the angles (A, B or C) is unknown, it can be found as long as the other two angles are known.

How to Find the Missing Angle in a Triangle

Finding the missing angle in a triangle is easy.

Question

What is the missing angle A in the triangle below?

Step-by-Step:

1

The angles add up to 180°.
A + 65° + 75° = 180°

2

Find A by subtracting the known angles from 180°.
A = 180° − 65° − 75° = 40°

Answer:

The missing angle A is 40°.

Lesson Slides

The slider below shows another real example of how to find the missing angle in a triangle.

How to Find the Missing Angle in an Equilateral Triangle

In the example above, we found the missing angle in a scalene triangle: a triangle where all three angles are different. It is even easier to find the missing angle in an equilateral triangle: where all three angles are equal to each other and all three sides are the same length. All three angles in an equilateral triangle are 60°.

How to Find the Missing Angle in an Isosceles Triangle

An isosceles triangle has two angles that are equal to each other.

An Equation to Find the Missing Angle

The interior angles of a triangle always add up to 180°. In this formula, A, B and C are the interior angles of a triangle. The formula...
A + B + C = 180°
... is an algebraic equation. A, B or C can be made the subject of the equation by subtracting the other two letters from both sides:

A = 180° − B − C

B = 180° − A − C

C = 180° − A − B

To find the missing angle:
  • Label each angle in the triangle with a letter.
  • The unknown letter will be to the left of the =. In the image above, A is the unknown angle. Choose the equation with A to the left of the =.
    A = 180° − B − C
  • Insert the values of the known letters into the right hand side of the equation. In the image above, B = 64° and C = 72°.
    A = 180° − 64° − 72°
  • Calculate the unknown angle.
    A = 44°