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Primary 6 · Angles · Question type 8.4

P6 Angles: Angles in a Composite Figure

At an endpoint of a shared line, the full angle is the sum of one angle from each shape.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Angles chapter8 question types · see the chapter

The lesson · 2 minutes 30 seconds

How do you find an unknown angle in a P6 composite figure?

Watch: a triangle standing on a square, sharing the line DC

Another worked example

A worked example

PQRS is a rhombus and angle QRS = 128°. QRT is an equilateral triangle built outward on side QR, so T lies outside the rhombus, and TP is drawn. Find angle PTR.

The working · Five lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. ∠PQR = 180° - 128° = 52° (angles between the parallel sides PQ and SR)
  2. ∠RQT = 60° (angles of an equilateral triangle QRT)
  3. ∠PQT = 52° + 60° = 112° (the two angles at the join Q)
  4. ∠QTP = (180° - 112°) ÷ 2 = 34° (base angles of isosceles triangle PQT, PQ, QR and QT all equal)
  5. ∠PTR = 60° - 34° = 26° (the two parts of ∠QTR)

The answer is 26°.

Practise · Modelled on top school exam questions

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Try it yourself

Join a rectangle and an isosceles triangle

Use the rectangle corner and equal sides to reach the asked angle.

DEFG is a rectangle and EFX is an isosceles triangle built outward on side EF, with EF = FX. Angle FEX = 62°. Find angle GFX.

°

Show the step-by-step solution
  1. ∠EFX = 180° - 62° - 62° = 56° (angle sum of isosceles triangle EFX)
  2. ∠GFX = 90° + 56° = 146° (right angle of the rectangle DEFG)

Ans: 146°

Keep practising

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Next, use angles between parallel sides. Angles in a Quadrilateral →

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