The idea in brief. A known angle on one parallel side DETERMINES the angle on the other. The two angles between a pair of parallel sides, one at each end of the side that joins them, add up to 180°, so a figure hands an angle across a gap the child has no other way of crossing. Everything else in the film is a consequence: the carried angle is split at the vertex it lands on, and its part finishes the triangle. In the lesson. And 62 degrees is the angle triangle QRS was missing.
Lesson video, with the working
Angles between parallel lines
3 min 33 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABCD is a trapezium with AB parallel to DC, and DEC is a triangle inside it. The figure is not drawn to scale. Angle ABC is 116°, angle BCE is 40° and angle EDC is 30°. Find angle DEC.
Angle DEC is 126°.
Ans: 126°
Example 1
PQRS is a trapezium with PQ parallel to SR. Angle PQR = 118° and angle QSR = 43°. Find angle x.
Angle x is 75°.
Ans: 75°
How to solve it
Find the triangle that holds the angle you want, and see which of its angles is missing: angle E C D.
A B and D C are parallel, so angle A B C and angle B C D add up to 180 degrees.
Subtract: angle B C D is 180 minus 116, which is 64 degrees.
Line C E cuts angle B C D, so angle E C D is 64 minus 40, which is 24 degrees.
The triangle now has 24 degrees and 30 degrees. Angle D E C is 180 minus 24 minus 30, which is 126 degrees.
P Q and S R are the parallel sides. 118 degrees and 62 degrees are the two angles between them. Together they are 180 degrees. And 62 degrees is the angle triangle Q R S was missing.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
How do you solve parallel lines angle questions in P6?
When a figure has a pair of parallel sides, the angle at one end of a slanting side tells you the angle at the other end.
What your child learns here
When a figure has a pair of parallel sides, the angle at one end of a slanting side tells you the angle at the other end. On this Primary 6 page that step leads into a triangle formed by a diagonal or another line.
Find the parallel sides from the arrowheads on the figure.
Use the property that the sum of each pair of angles between the parallel sides is 180°.
Use the fact that a rhombus's diagonal cuts its corner into two equal angles.
Finish with the angle sum of a triangle, writing the reason in a bracket on each line.
Does the answer make sense?
The two angles between the parallel sides, at either end of one slanting side, must add up to 180°, so one is acute and the other obtuse unless both are 90°. Any triangle your child uses at the end must have its three angles totalling exactly 180°.
How to practise these questions
The Basic questions train moving an angle across parallel sides in quadrilaterals such as rhombuses, then closing with a triangle's angle sum. Intermediate questions add an extended side or an isosceles triangle attached to the figure. Challenge questions need both pairs of parallel sides, or an angle added from two shapes at one vertex. If an angle refuses to cross the parallel lines, read the written step-by-step solution together.
Questions parents ask
Will my child learn corresponding or interior angles? Not at primary level: these words are not in the MOE primary syllabus. Our lessons name the property through the figure: the two angles between a pair of parallel sides add up to 180°.
How does my child spot parallel sides on a figure? Parallel sides are marked with matching arrowheads. Two sides carrying the same arrowheads are parallel, even when the drawing makes them hard to judge by eye.
Can my child draw extra lines to help find the angle? The Primary 6 syllabus outcome is finding unknown angles without additional construction of lines, so these questions are set to be solved with the lines already drawn.
