Angles in a Triangle
Angles in a Triangle is a key geometry topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on finding angles in a triangle, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. The angles in a triangle add up to 180°.
Free downloads
These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
The three angles inside any triangle always add to \(180^\circ\). This single fact underpins a great deal of geometry, and it holds no matter what shape the triangle is.
Particular triangles give extra information. An equilateral triangle has three equal angles of \(60^\circ\). An isosceles triangle has two equal sides and two equal base angles, which is what makes those questions solvable.
A right-angled triangle contains one \(90^\circ\) angle, so the other two must add to \(90^\circ\). Recognising which type of triangle is shown is usually the first step in finding a missing angle.
Revision notes
The angle sum
The three interior angles of any triangle add to \(180^\circ\).
So if two angles are \(50^\circ\) and \(70^\circ\), the third is \(180 - 120 = 60^\circ\).
Isosceles triangles
Two equal sides mean two equal angles, and those equal angles are opposite the equal sides.
If the apex angle is \(40^\circ\), the two base angles share the remaining \(140^\circ\), giving \(70^\circ\) each. Halving the remainder is the standard method.
Exterior angles
An exterior angle of a triangle equals the sum of the two opposite interior angles.
This follows from the straight line rule and often saves a step. It is also a valid reason to quote in an exam answer.
Key points
- Angles in a triangle add to \(180^\circ\).
- An equilateral triangle has three \(60^\circ\) angles.
- An isosceles triangle has two equal angles.
- Equal angles are opposite equal sides.
- A right-angled triangle's other two angles sum to \(90^\circ\).
- An exterior angle equals the sum of the opposite interior angles.
Worked examples
Example 1
Two angles of a triangle are \(65^\circ\) and \(48^\circ\). Find the third.
Working
Example 2
An isosceles triangle has an apex angle of \(50^\circ\). Find each base angle.
Working
Example 3
A right-angled triangle has one angle of \(35^\circ\). Find the third angle.
Working
Common mistakes
Forgetting the right angle counts towards the 180.
In a right-angled triangle the other two angles add to 90, not 180.
Not halving in an isosceles triangle.
The remaining amount is shared between two equal angles, so divide by 2.
Assuming a triangle is isosceles from the diagram.
Look for the dashes marking equal sides rather than judging by eye.
Omitting the reason.
State that angles in a triangle add to 180 degrees to earn the reasoning mark.
Exam tips
- Identify the type of triangle before calculating.
- Look for dashes marking equal sides.
- Halve the remainder for isosceles base angles.
- Give the angle fact as your reason every time.
Key terms
- Interior angle
- An angle inside a shape.
- Isosceles
- A triangle with two equal sides and two equal angles.
- Equilateral
- A triangle with three equal sides and angles.
- Exterior angle
- The angle between a side and the extension of another side.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.