Angles in triangles and quadrilaterals: GCSE Practice
Angles and Bearings
Angles in triangles and quadrilaterals
50 self-marking GCSE and IGCSE practice questions on Angles in triangles and quadrilaterals, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.
Sample Angles in triangles and quadrilaterals questions
A few of the 50 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 11 markGrade 2-3
A diagram shows a triangle with its three angles labelled 80°, 60°, and 50°.
The diagram is wrong. Explain why.
Show the worked solution
The angles in any triangle must add up to 180°.
What are the common mistakes in Angles in triangles and quadrilaterals?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Uses an incorrect total for the sum of angles in the given configuration
Used 180° instead of 360° for the sum of angles in a quadrilateral
Uses the wrong angle fact/theorem for the configuration shown (e.g. alternate vs corresponding angles)
Assumed opposite angles are equal (only true for cyclic quadrilaterals and parallelograms) instead of using the quadrilateral angle sum of 360°
Confuses an exterior angle with the third interior angle of a triangle
Calculated the third interior angle (180 − the two given angles) instead of the exterior angle (sum of the two opposite interior angles)
Quick answers about Angles in triangles and quadrilaterals
How many Angles in triangles and quadrilaterals practice questions are there?
There are 50 self-marking GCSE and IGCSE Maths questions on Angles in triangles and quadrilaterals, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
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80°+60°+50°=190°, which is not 180°, so this triangle is impossible.
Question 22 marksGrade 3-4
The diagram shows an isosceles triangle DEF, where DF=EF (diagram not drawn to scale).
(a) Work out the size of angle x.
(b) Give a reason for your answer.
Show the worked solution
Since DF=EF, triangle DEF is isosceles, so the base angles at D and E are equal. B1
x=30
Question 33 marksGrade 4-5
The diagram shows triangle XYZ, with side YZ extended to a point D (diagram not drawn to scale). Angle X=47° and angle XYZ=32°.
(a) Work out the size of the exterior angle x, marked at YZD.
(b) Give a reason for your answer.
Question 43 marksGrade 5-6
For each statement, decide whether it is always true, sometimes true, or never true.
(a) An isosceles triangle has a right angle.
(b) The three angles of a triangle sum to 180°.
(c) A triangle can have two obtuse angles.
Question 55 marksGrade 6-7
ABC and BCD are both isosceles triangles, with AB=BC and BC=CD.
B, C and D lie in a straight line configuration such that angle BCD is the angle at C in triangle BCD.
Angle CAB=81°.
Angle BCD is 4 times the size of angle ABC.
Find the ratio angle ABC : angle CBD. Give your answer in the form 1:n.
Question 65 marksGrade 6-7
Triangle ABC has angles of size a° (at A), b° (at B) and c° (at C).
A line is drawn through C, parallel to AB, extending in both directions.
a) Using angle facts, explain why the angle on the line at C, on the same side as angle a°, is equal to a°. What is this angle fact called?
b) Use the diagram and your answer to part (a) to show that the angles of a triangle add up to 180°. Give a reason for each statement you make.