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Finding A Missing Angle in an Isosceles Triangle

(KS2, Year 6)

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

the interior angles of a triangle add up to 180°.
two angles in the isosceles triangle are equal to each other.

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.

missing angles of an isosceles triangle

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? missing angles of an isosceles triangle vertex example

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. missing angles of an isosceles triangle vertex step 1

missing angles of an isosceles triangle vertex step 1

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°.

Lesson Slides

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

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? missing angles of an isosceles triangle base example

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. missing angles of an isosceles triangle base step 1

missing angles of an isosceles triangle base step 1

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°.

What Is an Isosceles Triangle?

An isosceles triangle is a triangle with two equal sides and two equal angles across from them.

The Parts of an Isosceles Triangle

An isosceles triangle has 2 equal sides. These sides are called legs. isosceles_triangle_legs

The third side is called the base. isosceles_triangle_base

An isosceles triangle has 2 equal angles. These are the angles between each leg and the base. They are called base angles. isosceles_triangle_base_angles