IGCSE Maths / Working with shape and space
Angles at a point and on a line
Edexcel International GCSE Maths (4MA1), chapter 11: Working with shape and space, specification point 4.1b. Free lesson.
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Use three angle rules to find missing angles: angles on a straight line total 180°, angles at a point total 360°, and vertically opposite angles are equal. State the rule clearly as well as giving the angle, because the reason earns a mark.
Angles on a straight line total 180°
A straight line is half a turn, so all the angles sitting side by side along it add to 180°. Subtract the known angles from 180° to find the missing one, then write the rule as your reason. Name an angle with three letters, such as ∠AOC. Saying “the angle at O” may not identify which angle you mean.
Angles at a point total 360°
A full turn around a point is 360°. When the angles fill the whole turn, subtract the known angles from 360°, not 180°. Check the picture before calculating: angles beside one straight line make 180°, while angles going all the way round a point make 360°.
Vertically opposite angles are equal
When two straight lines cross, the angles facing each other across the crossing are vertically opposite angles. They are equal. This can give you a missing angle directly, without calculating the other angles around the point. “Vertically opposite” means facing across the crossing, not simply being above or below another angle.
Write the reason for every angle
A correct number is not always enough. Put the matching reason beside your calculation. If you use two rules to find one angle, name both rules in the working. Angles on a straight line add up to 180°. Angles at a point add up to 360°. Vertically opposite angles are equal.
More lessons in Working with shape and space
- Angles in parallel lines
- Angle sum of a triangle
- 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