Finding an unknown angle in a four-sided figure is in the Primary 5 Parallelogram, Rhombus and Trapezium 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
Quadrilaterals
2 min 44 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABCD is a parallelogram. Angle BAD is 116°. Find angle ADC.
Angle ADC is 64°.
Ans: 64°
Example 1
PQRS is a trapezium with PQ parallel to SR. Angle PSR is 108°. True or false: angle SPQ = 108°.
Angle SPQ = 108° is False.
Ans: False
How to solve it
Name the shape and find the parallel sides. The arrowheads show which sides are parallel.
Find the pair of angles between two parallel sides. Here angle B A D and angle A D C are that pair.
The sum of each pair of angles between 2 parallel sides is 180 degrees.
Subtract: angle A D C is 180 minus 116, which is 64 degrees.
Opposite angles of a parallelogram are equal, so angle B C D is 116 degrees. Write the property in the bracket.
The arrowheads say P Q and S R are parallel. 108 and 72 are the two angles between them. Between a pair of parallel sides, the two angles add up to 180 degrees.
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 P5 parallelogram angle questions?
This page turns the Primary 5 properties of the parallelogram, rhombus and trapezium into angle facts.
What your child learns here
This page turns the Primary 5 properties of the parallelogram, rhombus and trapezium into angle facts. Your child finds a missing corner one property at a time and judges whether a statement about the angles is true.
Opposite angles of a parallelogram are equal, and a rhombus keeps this property because it is a parallelogram.
Two neighbouring corners of a parallelogram lie between a pair of parallel sides, so they add up to 180°.
A trapezium has only one pair of parallel sides, so only the angles between that pair add up to 180°.
A rhombus with one right angle has four right angles, so it is a square.
All four sides of a rhombus are equal, so a diagonal makes two isosceles triangles inside it.
Does the answer make sense?
Angle JML is the corner opposite angle JKL, so it must be 58° and nothing else. The two remaining corners of the rhombus are then 180° minus 58°, which is 122° each, since each one sits beside a 58° corner between parallel sides.
How to practise these questions
Question 1, free to everyone, is rhombus JKLM with angle JKL of 58°, and your child finds angle JML, the corner opposite it. The Basic questions train each property on its own and ask your child to judge true-or-false statements about a parallelogram or a trapezium. The Intermediate questions add a diagonal across a rhombus, or a right angle that makes a rhombus a square. The Challenge questions combine a diagonal's isosceles triangle with the parallel sides, and one asks for two statements to be judged at once. If your child is stuck, open its worked solution and name the property used on each line.
Questions parents ask
Are the opposite angles of a trapezium equal? Not in general. A trapezium has one pair of parallel sides, so the two angles between them add up to 180°, but its opposite angles need not match.
Why are some questions true or false? Judging a statement makes your child test a property against the numbers instead of only calculating. The working finds the angle first, then compares it with the claim.
Does Primary 5 teach the diagonals of these shapes? No diagonal property is listed for Primary 5. When a diagonal is drawn here, your child works through the triangles it makes, using equal sides and the angle sum.
