The idea in brief. Two shapes that share an edge share both of its ends, and an angle at a shared corner is one angle from each shape. Where the angle across the join is wanted, the two are added; where it is given, one of them is taken off. That is the whole of what a composite figure asks, and it is why the P6 outcome says "composite" and nothing else. In the lesson. One corner point, one angle from each shape.
Lesson video, with the working
Angles in a composite figure
2 min 59 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
ABCD is a square and DCE is an isosceles triangle with DE and DC equal. Angle DCE is 65°. Find angle ADE.
Angle ADE is 140°.
Ans: 140°
Example 1
PQRS is a square and QRT is a triangle. Angle PQT = 137° and angle QTR = 62°. Find angle QRT.
Angle QRT is 71°.
Ans: 71°
How to solve it
Find what the two shapes share. The square and the triangle share the line D C, so D and C are corners of both.
Work inside the shape whose angles are not marked. D E and D C are equal, so angle D E C is 65 degrees too.
Triangle D C E has 180 degrees in all, so the angle at D is 180 minus 65 minus 65, which is 50 degrees.
Angle A D E has two parts at D: the square's 90 degrees and the triangle's 50 degrees.
Add them: 90 plus 50 is 140 degrees.
The 137 degrees at Q crosses the line Q R. Inside it, 90 degrees is the right angle of the square. And 47 degrees is the triangle's. One vertex, one angle from each shape.
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 composite figure angle questions in P6?
A composite figure is two or more shapes joined along a line.
What your child learns here
A composite figure is two or more shapes joined along a line. The Primary 6 syllabus asks children to find unknown angles in such figures without drawing extra lines, and the key move here is splitting an angle at the join into one part from each shape.
Find the line the shapes share, and the corners that belong to both.
Use each shape's own properties: 90° corners for a square or rectangle, 60° for an equilateral triangle, equal base angles for an isosceles triangle.
Split an angle at the join into one part from each shape, then add or subtract.
Find unknown angles without drawing any extra lines, as the syllabus requires.
Does the answer make sense?
When the angle asked for spans the join, it must be bigger than each shape's own corner there, since it is one part from each shape added together. When it is the corner of a single triangle, your child can check that triangle's three corners total 180°.
How to practise these questions
The Basic questions train splitting an angle at a shared corner into the rectangle's part and the triangle's part. Intermediate questions add squares, parallelograms and rhombuses with triangles attached, and an answer built from one angle in each shape. Challenge questions need an extra triangle formed inside the figure, or a corner found across parallel sides before the join can be used. When the angle across a join is unclear, read the written step-by-step solution together.
Questions parents ask
What is a composite figure in P6 maths? A composite figure is made from two or more simple shapes joined together, such as a triangle standing on a square. The Primary 6 syllabus lists square, rectangle, triangle, parallelogram, rhombus and trapezium as the shapes involved.
Are composite figure angle questions in the PSLE syllabus? Finding unknown angles in composite figures is a Primary 6 geometry outcome in the MOE syllabus, so it is part of the syllabus the PSLE is set on.
What should my child look at first in a composite figure? Find the line the shapes share and the corners that belong to both. Then use each shape's own properties at those corners, one shape at a time.
