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Quadrilaterals and centres of triangles・Form 3 maths

Find angles in a parallelogram

A standard method from Quadrilaterals and centres of triangles: the steps and worked examples.

Steps

  1. Opposite angles are equal.
  2. Adjacent angles add to 180° (int. ∠s, AB // DC).
  3. Write the reason in brackets after each angle you find.

Worked examples

Example 1: Find angles in a parallelogram: ABCD is a parallelogram with ∠A = (3x + 10)° and ∠C = (5x − 30)°. Find x and ∠B.
∠A = ∠C                 (opp. ∠s of //gram)
3x + 10 = 5x − 30
     40 = 2x
      x = 20
∠A = 70°
∠B = 180° − 70° = 110°  (int. ∠s, AD // BC)

For the whole topic, read Quadrilaterals and centres of triangles: key points, common mistakes and how the DSE tests it.

Other methods in this topic

Mid-point theorem (NF)Quadrilaterals and centres of trianglesWhich centre is which (NF)Quadrilaterals and centres of triangles