Geometry and measuresKey Stage 3

Angles in an isosceles triangle with algebra

Use equal base angles to form and solve equations.

  • Identify the equal sides before choosing the equal angles.
  • Equate the two base-angle expressions, or use both base angles in the total.

Example 1

The marked sides are equal. Find .

The two base angles are equal.Apply this to both sides.
The two base angles are equal.
Apply this to both sides.

Example 2

Find in the isosceles triangle.

The equal base angles and the vertex angle add to 180°.Apply this to both sides.Apply this to both sides.
The equal base angles and the vertex angle add to 180°.
Apply this to both sides.Apply this to both sides.

Your turn

Question 1

The marked sides are equal. Find .

Check answer
The two base angles are equal.Apply this to both sides.
The two base angles are equal.
Apply this to both sides.
Question 2

Find in the isosceles triangle.

Check answer
The equal base angles and the vertex angle add to 180°.Apply this to both sides.Apply this to both sides.
The equal base angles and the vertex angle add to 180°.
Apply this to both sides.Apply this to both sides.
Question 3

The marked sides are equal. Find .

Check answer
The two base angles are equal.Apply this to both sides.
The two base angles are equal.
Apply this to both sides.
Question 4

Find in the isosceles triangle.

Check answer
The equal base angles and the vertex angle add to 180°.Apply this to both sides.Apply this to both sides.
The equal base angles and the vertex angle add to 180°.
Apply this to both sides.Apply this to both sides.
Question 5

The marked sides are equal. Find .

Check answer
The two base angles are equal.Apply this to both sides.
The two base angles are equal.
Apply this to both sides.
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