Primary 6 · Measurement & Geometry
P6 angles in geometrical figures
In P6, your child finds unknown angles in figures built from squares, rectangles, triangles, parallelograms, rhombuses and trapeziums. Every angle comes from what is given, never from how the drawing looks.
- Taught in
- Term 1
- Syllabus
- 1 skill
- Usual slip
- Trusting the drawing
What your child learns in P6 angles in geometrical figures
One skill, each with what it looks like on a worksheet.
See the syllabus wording
- finding unknown angles, without additional construction of lines, in composite geometric figures involving square, rectangle, triangle, parallelogram, rhombus, trapezium
Unknown angles in composite figures
Your child finds a missing angle in a figure made of two or more shapes, one rule at a time. The figure is not drawn to scale, so every angle comes from what is given or marked.
Words to know
- Not to scale
- The drawing's angles and lengths may be off. Use only what is given.
- ∠ABC
- The angle at B, between BA and BC. The middle letter is the corner.
- Angle sum
- The three angles of any triangle add up to 180°.
- Isosceles triangle
- A triangle with two equal sides. The angles facing them are equal.
The sentence that costs the mark
In triangle PQR, ∠QPR = 48° and ∠QRP = 46°. The figure is not drawn to scale. Find ∠PQR.
What the working usually does
∠Q =the drawing=90°
Reads the angle off the picture. The corner at Q looks square, so it writes 90°.
What the question asked
∠Q =180° − 48° − 46°=86°
Works it out from the two given angles, using the angle sum of a triangle.
90° is a clean, believable answer, the corner really does look square, and 86° is only 4° away, so nothing on the page looks wrong. Only the given angles may be used.
The same P6 angles in geometrical figures question, worked properly
Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.
ABCD is a square. DE = DC and ∠CDE = 40°. Find ∠DAE.
- Start the angle chase at D. A square's corner is 90° and the marked angle at D is 40°, so ∠ADE = 90° + 40° = 130°.
- DA = DC, because they are sides of the square. The marks show DC = DE, so DA = DE and triangle ADE is isosceles.
- The angle sum of a triangle is 180°. So the two equal angles share 180° − 130° = 50°.
- The two angles are equal, so ∠DAE = 50° ÷ 2 = 25°.
- So the missing angle is 25°.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeThree quick P6 angles in geometrical figures questions
Try them together, then tap to check.
Question 1
One angle of a parallelogram is 72°. What are its other three angles?
Show answer
Answer108°, 72° and 108°. Opposite angles are equal, and neighbouring angles add up to 180°.
Question 2
In an isosceles triangle, the angle between the two equal sides is 50°. Find each of the other two angles.
Show answer
Answer65° each. 180° − 50° = 130°, and 130° ÷ 2 = 65°.
Question 3
Two angles of a triangle are 35° and 57°. The third looks like a right angle. What is it?
Show answer
Answer88°. 180° − 35° − 57° = 88°, so it is not a right angle.
Helping at home
How to tell it has clicked
Ask your child where each angle in their working came from. Every number should point to a given or a rule, such as "the angle sum of a triangle". "It looks like 90°" is the slip.
Try this tonight
Draw a triangle whose top corner is nearly, but not quite, a square corner, and write two of its angles on it. Ask your child for the third. If they say 90°, ask them to prove it from the numbers on the page.
Before and after P6 angles in geometrical figures
Builds on
Primary 5 AnglesBuilds on
Primary 5 Properties of TrianglesBuilds on
Primary 5 Parallelogram, Rhombus and TrapeziumYou are here
Primary 6 Angles in Geometrical Figures
Finds unknown angles in composite figures
More in Primary 6
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.