Picture a triangle. Two of its corners have been measured for us: one corner is 50° and one corner is 60°. Nobody has measured the third corner yet.

Let's look at three very different triangles together. Each one is already built and its three corners are measured. As we look at each, add up the three numbers in your head and see what you notice.

Three completely different triangles: a wide flat one, a tall thin one, and a right-angled one. What is the same about all three?

Now that we know the three angles of any triangle add to 180°, let's test it on fresh triangles. We take turns coming up to drag the corners. Watch the three angles change but the total stay at 180°.

Before we start, look at how we solve an isosceles triangle when we are only told the top angle.

Finding equal base angles

• The top angle is 30°. The two base angles are equal to each other.
• First take the top angle away from 180: 180 − 30 = 150. That 150 is shared between the two base angles.
• Now split it into two equal halves: 150 ÷ 2 = 75. So each base angle is 75°.

That is the two-move method you used in your copy just now: take the top away from 180, then share the leftover equally. Now we take on five triangles, each one a step trickier. Predict each missing angle before we press Check.