Primary 6 · Angles · Question type 8.5

P6 Angles: Angles Between Parallel Lines

Angles between the same pair of parallel sides add up to 180°, allowing the missing angle to be calculated.

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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 56 seconds

How do parallel lines help you find angles in P6?

Watch: a trapezium with 116° at one corner and a triangle inside it

Another worked example

A worked example

ABCD is a trapezium with AB // DC and the diagonal BD drawn. Angle DAB = 126°, angle ABC = 97° and angle ADB = 23°. Find angle DBC.

The working · Four lines

The step-by-step working

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

∠ADC = 180° - 126° = 54° (angles between the parallel sides AB and DC)
∠BDC = 54° - 23° = 31° (the two parts of ∠ADC)
∠BCD = 180° - 97° = 83° (angles between the parallel sides AB and DC)
∠DBC = 180° - 83° - 31° = 66° (angle sum of triangle BCD)

The answer is 66°.

Practise · Modelled on top school exam questions

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A diagonal in a parallelogram

Use the parallelogram's angle and diagonal properties to find the unknown angle.

ABCD is a parallelogram with diagonal BD drawn. Angle BAD = 118° and angle ADB = 26°. Find angle DBC.

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∠ADC = 180° - 118° = 62° (angles between the parallel sides AB and DC)
∠BDC = 62° - 26° = 36° (the two parts of ∠ADC)
∠BCD = ∠BAD = 118° (opposite angles of a parallelogram)
∠DBC = 180° - 118° - 36° = 26° (angle sum of triangle BCD)

Ans: 26°

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Next, use the full 360° around a point. Angles in a Folded Figure →

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