IGCSE Maths / Working with shape and space
Angle sum of a triangle
Edexcel International GCSE Maths (4MA1), chapter 11: Working with shape and space, specification point 4.1c. Free lesson.
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The angles inside any triangle add up to 180°. You can use this property to find a missing angle and combine it with other angle rules in multi-step questions.
How to find the third angle
The three interior angles of a triangle always total 180°, whatever the triangle’s shape. Subtract both known angles from 180° to find the third. Give the property as your reason, because the correct number and the reason can earn separate marks. Check your answer by adding all three angles: the total should be 180°.
Why the angles add up to 180°
Draw a line through the triangle’s top corner, parallel to its base. The sides of the triangle cross these parallel lines, making angles that match the two base angles. They are equal because alternate angles between parallel lines are equal. The three angles now sit together on a straight line, so they add up to 180°. This explains where the triangle property comes from. The angle on the straight line between the two matching angles is the triangle’s top angle.
Why a triangle has at most one obtuse angle
An obtuse angle is bigger than 90°. Two obtuse angles would already total more than 180°, but all three angles in a triangle must total exactly 180°. That leaves no room for the third angle, so a triangle cannot have two obtuse angles. If your answer gives a triangle two obtuse angles, check your working.
How to combine angle rules
Some questions need more than one step. First use the triangle angle sum to find the missing angle in the triangle. Then use the next angle rule. For example, vertically opposite angles are equal when two straight lines cross. Write one line of working and one reason for each step. A correct number with only one reason may earn the mark for one step, but not both.
More lessons in Working with shape and space
- Angles at a point and on a line
- Angles in parallel lines
- Exterior angle of a triangle
- Angles in special triangles
- Angle sum of a quadrilateral
- Properties of quadrilaterals
- Writing geometrical reasons
- Angle sum of a polygon
- Interior and exterior angles of regular polygons
- Finding the number of sides from an angle
- Irregular polygon angle problems
- Perimeter and area of rectangles and triangles
- Area of a parallelogram
- Area of a trapezium
- Names of solids: faces, edges and vertices
- Surface area of a cuboid
- Surface area of a triangular prism
- Volume of a prism
- Compound prisms and volume units
- Time intervals, money and currency
- Converting units of length, area and volume