How to Find Missing Angle in an Isosceles Triangle

Finding a Missing Angle in an Isosceles Triangle

To find the missing angle of an isosceles triangle, use two facts:

The image below shows an isosceles triangle. The vertex angle is labelled A and the two base angles (which are equal to each other) are labelled B.

If either of the angles (A or B) is unknown, it can be found as long as the other angle is known.

How to Find the Missing Angle in an Isosceles Triangle

Finding the missing angle in an isosceles triangle is easy.

The method is different depending on whether the missing angle is a vertex angle or a base angle.

Finding the Missing Vertex Angle

The vertex angle is the angle between the two sides of equal length.

Question

What is the missing angle A in the isosceles triangle below?

Step-by-Step:

1

Which angle is which?

The missing angle A is between the two sides of the same length. It is a vertex angle.

The other two angles are base angles and are equal to each other.

2

The angles add up to 180°.

A + 70° + 70° = 180°

3

Find A by subtracting the known angles from 180°.

A = 180° − 70° − 70° = 40°

Answer:

The missing angle A is 40°.

Slider

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

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Finding a Missing Base Angle

The base angles are the two angles that are not between the two sides of equal length.

Question

What is the missing angle B in the isosceles triangle below?

Step-by-Step:

1

Which angle is which?

The missing angle B is not between the two sides of the same length. It is a base angle.

The 30° angle is the vertex angle because it is between the two sides of the same length.

The other angle that is not labelled is the other base angle. It is equal to B.

2

The angles add up to 180°.

30° + B + B = 180°

30° + 2B = 180°

3

Subtract the known angle from both sides of the equation.

30° + 2B − 30° = 180° − 30°

2B = 150°

4

Divide both sides of the equation by 2.

2B ÷ 2 = 150° ÷ 2

B = 75°

Answer:

The missing angle B is 75°.

Slider

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

Open the slider in a new tab

See Also

What is a triangle? What is an isosceles triangle? What is an angle?