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Primary 6 · Angles · Question type 8.8

P6 Angles: Mixed Angle Questions

Read the marks on the figure first, then choose the property needed for each part of the question.

Try the question yourself, or watch the lesson first.

Primary 6, on the MOE Primary Mathematics syllabus.

In the Angles chapter8 question types · see the chapter

The lesson · 1 minute 52 seconds

How do you solve mixed P6 angle questions?

Watch: a trapezium, two equal sides and a straight line in one question

Another worked example

A worked example

PQRS is a trapezium with PQ // SR. PRS is an isosceles triangle with PR = RS. Angle PQR = 108°. Angle PRS = 54°. Find angle SPQ.

The working · Five lines

The step-by-step working

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

  1. ∠QRS = 180° - 108° = 72° (angles between the parallel sides PQ and SR)
  2. ∠RPS = ∠RSP = (180° - 54°) ÷ 2 = 63° (base angles of isosceles triangle PRS, PR and RS equal)
  3. ∠QRP = 72° - 54° = 18° (the two parts of ∠QRS)
  4. ∠QPR = 180° - 108° - 18° = 54° (angle sum of triangle PQR)
  5. ∠SPQ = 63° + 54° = 117° (the two parts of ∠SPQ)

The answer is 117°.

Practise · Modelled on top school exam questions

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Choose the angle properties

Identify the properties needed before combining them in this mixed figure.

AC and BD are straight lines crossing at E. In triangle ABE, angle EAB = 56° and angle ABE = 48°. In triangle CED, angle ECD = 53°. Find angle EDC.

°

Show the step-by-step solution
  1. ∠AEB = 180° - 56° - 48° = 76° (angle sum of triangle ABE)
  2. ∠CED = ∠AEB = 76° (vertically opposite angles)
  3. ∠EDC = 180° - 53° - 76° = 51° (angle sum of triangle CED)

Ans: 51°

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