The idea in brief. A four-sided figure's MARKS say which property you may use on it. Arrowheads say two sides are parallel, and then the two angles between that pair add up to 180°; a small box says a corner is 90°. In a parallelogram the angles across the figure are equal as well, in a trapezium they are not, and it is the marks, not the look of the drawing, that tell the two apart. In the lesson. Between a pair of parallel sides, the two angles add up to one hundred and eighty degrees.
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 10 open in the free trial, each with its full working.
∠MNK = ∠KLM = 65° (opposite angles of a parallelogram)
∠LMN = 180° − 65° = 115° (angles between the parallel sides KL and MN)
115° is not less than 90°, so the statement is False
Answer: False; two of the angles are 115°
For parents
How do you solve parallelogram angle questions in P6?
A quadrilateral is a four-sided figure.
What your child learns here
A quadrilateral is a four-sided figure. The Primary 6 syllabus names the special ones, and this page uses their angle facts: which corners match and which pairs make 180°.
Read the arrowheads that show parallel sides and the marks that show equal sides.
Use the property that the two angles between a pair of parallel sides add up to 180°.
Use the property that opposite angles of a parallelogram are equal; a rhombus is a parallelogram, so this holds there too.
Name the angle asked for carefully, since a diagonal can split a corner into two smaller angles.
Does the answer make sense?
Opposite corners of a parallelogram or rhombus are equal, and neighbouring corners add up to 180°, so a corner next to an obtuse one is acute. A diagonal splits a corner into two parts that add back to the whole corner, and in a rhombus your child will find those parts equal.
How to practise these questions
The Basic questions train the angle properties of parallelograms, squares and other quadrilaterals, often by judging whether a statement is true. Intermediate questions add a rhombus with a diagonal drawn, and deciding what extra information would make a shape a square or a parallelogram. Challenge questions ask for half of a corner, reached through the isosceles triangle that a diagonal creates. If a quadrilateral property is not clicking, read the written step-by-step solution.
Questions parents ask
Is a rhombus a parallelogram? Yes. A rhombus has two pairs of parallel sides, so it is a parallelogram with all four sides equal as well. Its opposite angles are equal and its neighbouring angles add up to 180°.
Does a trapezium have equal opposite angles? Not in general. A trapezium has only one pair of parallel sides, so the property it gives is that the two angles between those parallel sides add up to 180°.
Can my child use the word quadrilateral? Yes. The MOE syllabus uses 'Special Quadrilaterals' as its Primary 6 geometry heading. Our lesson also calls these shapes four-sided figures.
