Following a route between parallel lines is in the Primary 5 Angles chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is chosen for Primary 5.
Lesson video, with the working
Angles Between Parallel Lines
3 min 34 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 2 open in the free trial, each with its full working.
∠QRS = 180° − 131° = 49° (angles between the parallel sides PQ and SR)
∠QSR = 180° − 59° − 49° = 72° (angle sum of triangle QRS)
Answer: 72°
For parents
How do you solve P5 angles between parallel sides questions?
This page applies the Primary 5 properties of the parallelogram, rhombus and trapezium to figures with a diagonal drawn.
What your child learns here
This page applies the Primary 5 properties of the parallelogram, rhombus and trapezium to figures with a diagonal drawn. Your child finds one angle from the parallel sides first, then uses it inside a triangle to reach the angle asked for.
Matching arrowheads on two sides mark them as parallel.
At the two ends of one slanting side, the pair of angles between the parallel sides adds up to 180°.
A diagonal splits a corner into two parts that add back to the whole corner.
Opposite angles of a parallelogram or rhombus are equal.
All four sides of a rhombus are equal, so a diagonal cuts it into two isosceles triangles.
The final step is usually the angle sum of a triangle, 180°.
Does the answer make sense?
In Question 1, angle QRS is 180° minus 131°, which is 49°, and an acute angle sitting beside an obtuse one is what the parallel sides should give. Triangle QRS then holds 59°, 49° and 72°, which add up to 180°, so angle QSR is 72°.
How to practise these questions
Question 1, free to everyone, is trapezium PQRS with PQ parallel to SR and the diagonal QS drawn: angle PQR is 131° and angle SQR is 59°, and your child finds angle QSR. The Basic questions train one step across the parallel sides followed by one triangle, in trapeziums and a rhombus. The Intermediate questions add a corner split by a diagonal or a line, so one part comes off before the triangle is used. When the route will not come, open its worked solution and follow the reason written on each line.
Questions parents ask
Does my child need to know corresponding or interior angles? No. Those names are not in the primary syllabus. Primary 5 words the property through the shape: each pair of angles between the parallel sides adds up to 180°.
Can my child draw an extra line to help? The Primary 5 outcome asks for unknown angles found without additional construction of lines. Every line the working needs is already on the figure.
Why start with the parallel sides? The parallel sides give the one angle the triangle is missing. Once that angle is known, the angle sum of the triangle finishes the question.
