GCSE & IGCSE maths practice

Angles in a triangle questions and answers

The angles in a triangle add up to $180°$ . In an isosceles triangle the two base angles are equal; in a right-angled triangle the other two angles add up to $90°$ . An exterior angle of a triangle equals the sum of the two interior angles opposite it.

15 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 10 Nov 2026.

Start the questions Angles and triangles: lesson Angles in parallel lines guide

Where angles in a triangle comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: derive and use the sum of angles in a triangle, and angles at a point, on a straight line and vertically opposite.
Cambridge IGCSE (0580)	Core and Extended: calculate unknown angles using the angle sum of a triangle (180°) and of a quadrilateral (360°), giving reasons.

The method

Add the angles you know and take them from 180°.
Isosceles: the base angles are equal.
Exterior angle = sum of the two opposite interior angles.
Algebra: add the expressions, set equal to 180°, and solve.

Angles in a triangle questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Two angles of a triangle are $50°$ and $70°$ . Find the third angle.

Question 2Warm-upFoundation

In an isosceles triangle, the angle between the two equal sides is $40°$ . Find each of the other two angles.

Question 9Warm-upFoundation

A right-angled triangle has an angle of $25°$ . Find the third angle.

Question 10Warm-upFoundation

What is the size of each angle in an equilateral triangle?

Exam-style

Question 3Exam-styleFoundation

A right-angled triangle has an angle of $35°$ . Find the third angle.

Question 4Exam-styleFoundation

The angles of a triangle are $2x$ , $3x$ and $4x$ . Find $x$ .

x =

Question 5Exam-styleFoundation

Two interior angles of a triangle are $45°$ and $65°$ . Find the exterior angle at the third vertex.

Question 6Exam-styleFoundation

In triangle ABC, angle A is $48°$ and the exterior angle at C is $130°$ . Find angle B.

Question 11Exam-styleFoundation

An isosceles triangle has one base angle of $68°$ . Find the angle at the top (between the equal sides).

Question 12Exam-styleFoundation

The angles of a triangle are $x$ , $x + 20$ and $2x$ (in degrees). Find $x$ .

x =

Question 13Exam-styleFoundation

The exterior angle of a triangle is $125°$ . One of the two opposite interior angles is $70°$ . Find the other.

Challenge

Question 7ChallengeFoundation

An isosceles triangle has base angles of $52°$ . Find the third angle.

Question 8ChallengeFoundation

The angles of a triangle are $x + 10$ , $2x$ and $3x - 40$ (in degrees). Find $x$ .

x =

Question 14ChallengeFoundation

In a right-angled triangle, the other two angles are in the ratio $2 : 3$ . Find the larger of these two angles.

Question 15ChallengeFoundation

In an isosceles triangle, the angle between the equal sides is 3 times the size of each base angle. Find the angle between the equal sides.

Common mistakes

Using 360° for a triangle.
Getting the wrong pair of equal angles in an isosceles triangle.
Finding x but not the angle the question asks for.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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