Basic Angle Properties (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

Basic angle properties

What are the basic angle properties?

• Angles around a point add up to 360°

• Angles that form a straight line add up to 180°

• Vertically opposite angles are equal

  • Vertically opposite angles occur when two lines intersect, as in the diagram below

What are the angle properties of triangles?

• The three interior angles inside any triangle add up to 180°

• If the triangle is isosceles then two angles will be equal

  • These will be the two angles opposite the two sides of equal length

• If the triangle is equilateral then all three angles will be equal

  • Each angle will equal 60°

• A right-angled triangle has one 90° angle

• The exterior angle of a triangle (180-the interior angle) is equal to the sum of the other two interior angles

  • You can remember this result, but it is also straight forward to work out

  • In the diagram below, angle c is (180-a-b) as angles in a triangle sum to 180

  • The exterior angle is (180-c) as angles on a straight line sum to 180

  • Therefore the exterior angle at c is (180-(180-a-b)) = a+b

What are the angle properties of quadrilaterals?

• The four interior angles inside any quadrilateral add up to 360°

• If the quadrilateral is a square or a rectangle then all the angles are equal to 90°

• You can use any symmetries of the quadrilateral to identify other equal angles

  • For a parallelogram (or rhombus), opposite angles are equal

  • For a kite, one pair of opposite angles are equal