Triangles

A triangle is the simplest shape with straight sides, yet it hides a powerful secret: no matter how stretched or squashed it looks, its three angles always add to the same total. This is a P5 topic, and combining that fact with the special triangles below lets you crack almost any "find the unknown angle" question without a protractor.

Parents: ask your child to name the triangle type and the angle fact before they reveal. The "Method tip" boxes name the exact rule a PSLE marker rewards.

By the end you'll be able to recognise the special triangles, use the angle sum of 180 degrees, and find unknown angles. Let's begin.

The three special triangles

Three triangle types come up again and again. An isosceles triangle has two equal sides and two equal angles. An equilateral triangle has all three sides equal and all three angles equal. A right-angled triangle has one angle of exactly 90 degrees.

Because an equilateral triangle has three equal angles that add to 180 degrees, each angle is 180 ÷ 3 = 60 degrees. That is a fact worth memorising.

The angle sum is 180 degrees

The most useful fact of all: the three angles of any triangle add up to 180 degrees. So if you know two angles, subtract them both from 180 to find the third.

For example, a triangle has angles 50 degrees, 60 degrees and x. Then x = 180 − 50 − 60 = 70 degrees. This works for every triangle, no matter its shape or size.

Using the isosceles triangle

An isosceles triangle has two equal angles (the base angles). If you know one of them, you know the other for free. Combine this with the 180-degree sum to find every angle.

For example, an isosceles triangle has a top angle of 40 degrees. The two base angles are equal, so together they are 180 − 40 = 140 degrees, and each base angle is 140 ÷ 2 = 70 degrees.

Finding unknown angles in figures

Harder questions combine triangle facts with the angle rules from straight lines. Work one step at a time: find an angle inside the triangle, then use a straight line or a point if the figure needs it.

For example, a triangle has angles 35 degrees and 65 degrees, so the third is 180 − 35 − 65 = 80 degrees. If that third angle sits on a straight line with another angle, the neighbour is 180 − 80 = 100 degrees.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. A triangle has angles of 70 degrees, 60 degrees and x. What is x?

   50 degrees130 degrees60 degrees

2. What is the size of each angle in an equilateral triangle?

   90 degrees60 degrees45 degrees

3. A right-angled triangle has one angle of 25 degrees. What is its third angle?

   65 degrees55 degrees75 degrees

4. An isosceles triangle has a top angle of 100 degrees. What is each base angle?

   40 degrees80 degrees50 degrees

5. An isosceles triangle has each base angle equal to 65 degrees. What is the top angle?

   50 degrees65 degrees130 degrees

6. A triangle has angles 30 degrees and 90 degrees. The third angle lies on a straight line with another angle. What is that neighbouring angle?

   120 degrees60 degrees90 degrees

See my score