Angle facts: using the outside angle inside the triangle
Your child knows the angles in a triangle add up to 180°, but uses an angle that sits outside the triangle in the sum. The answer is often a small, tidy number that looks believable. Geometry questions chain angle facts together, so one wrong fact early on spoils the rest.
What it looks like
Points A, B and C lie on a straight line. Point D is above the line so that BCD is a triangle. ∠ABD = 128° and ∠BCD = 34°. Find ∠BDC.
- ∠DBC = 180° − 128° = 52° (angles on a straight line)
- ∠BDC = 180° − 52° − 34° = 94° (angles in a triangle)
Why 18° is wrong: The 128° outside the triangle was used as if it were inside it: 180° − 128° − 34° = 18°.
Why children do it
- The given angle is marked on the figure right next to the triangle, so it looks like part of it.
- Children apply "180°" without checking whether the angles they are adding are inside the shape.
- The step through the straight line (180° − the given angle) feels like an extra step, so it gets skipped.
How to fix it at home
- Ask your child to shade the triangle and check that every angle in the sum is inside the shaded part.
- Have your child write the reason next to each step, such as "angles on a straight line".
- Practise the four totals until they are automatic: straight line 180°, triangle 180°, quadrilateral 360°, around a point 360°.
- Check the answer by eye: an angle that looks obtuse in the figure should not come out as 18°.
Questions parents ask
Do PSLE markers want the angle reasons written?
Clear working is what earns method marks. Short reasons also help your child catch the mistake while writing.
The figures are not drawn to scale. Can my child still check by eye?
Only roughly. A figure that is not to scale can still show whether an angle is acute or obtuse, which is often enough to catch this slip.
Where it shows up
Other careless mistakes
Stop losing marks to the same mistake.
Three PSLE questions, free, no sign-up. You’ll see exactly where the marks went. Then 7 days of everything for S$4.99.