Two figures joined, and the angle where they meet 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 and notes
Angles in a Composite Figure
2 min 59 s
This lesson is shared with Primary 6.
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 find P5 angles in composite figures questions across a join?
These figures join a triangle to one side of a square, rectangle, parallelogram or rhombus.
What your child learns here
These figures join a triangle to one side of a square, rectangle, parallelogram or rhombus. The angle at the shared corner is made of one angle from each shape, so your child adds or takes away the shape's own corner and then uses the triangle's angle sum. Every fact needed is a Primary 5 property of triangles and four-sided figures, used without drawing any extra lines.
At a shared corner, the angle across the join is the four-sided figure's angle plus the triangle's angle.
A square or rectangle gives a 90° corner; a parallelogram or rhombus gives the angle printed or found from its parallel sides.
An equilateral triangle gives 60° at every corner.
An isosceles triangle has two equal base angles opposite its two equal sides.
When a triangle is built on a side of a square, its equal side matches the square's side, which can make a new isosceles triangle across the join.
Does the answer make sense?
In Question 1, the triangle's angle at C is 152° minus 90°, which is 62°. Its other two angles are equal, so each is 180° minus 62°, halved, which is 59°. Then 59° + 59° + 62° comes to 180°, as every triangle must.
How to practise these questions
Question 1 is free: an isosceles triangle stands outside a rectangle on side BC, the angle across the join is 152°, and your child takes off the rectangle's 90° and halves what is left of the triangle. It is the one Basic question. The Intermediate questions add a rectangle's corner to a triangle's angle, build an equilateral triangle on a square so that the square's side and the triangle's side are equal and a new isosceles triangle appears, or set the triangle on a parallelogram or a rhombus. The two Challenge questions use two triangles: one where a line crosses the square, and one where a line from an equilateral triangle's tip to the far corner of a rhombus splits the triangle's corner. Ask your child to shade the two shapes in different colours before starting.
Questions parents ask
Are composite figures in the Primary 5 syllabus? The MOE syllabus names composite figures for angles at Primary 6. Every step here uses Primary 5 properties of triangles, squares, rectangles, parallelograms and rhombuses, so the page practises those properties working together.
Why does an equilateral triangle on a square make an isosceles triangle? The triangle's sides equal the square's side. A line from the triangle's tip to a far corner of the square therefore joins two equal sides, and the triangle it closes has two equal angles.
Should my child draw an extra line? No. The syllabus asks for unknown angles without additional lines, and every line these questions need is already drawn.
