Imagine a triangle sitting on a straight line, with two lines crossing beside it. Some angles are marked; one is missing.

Which angle do you think we could work out first — and why can't we always reach for the one we most want to know?

Watch four figures on the board. In each one, an angle is missing. Look for which fact helps:

• angles on a straight line make 180°
• the three angles of a triangle make 180°
• vertically opposite angles (where two lines cross, the angles facing each other) are equal

Be ready to say which fact you would reach for on each figure.

Today we work through one figure together, step by step. A triangle sits on a straight line, and two lines cross beside it. We know two of the triangle's angles: 65° and 40°.

We will find the angles in a set order. First we find the triangle's third angle. Then we find the angle beside it on the line. Last we find the angle vertically opposite that one. Say which fact we are using before each step.

Today we crack a chained figure where each angle we find unlocks the next. We solve them in this order:

• the third angle of a triangle whose other two are 40° and 75°
• the angle beside it on a straight line
• the angle vertically opposite where two lines cross
• and last, a separate straight line at its own point, split into three marked angles: a right angle (90°), an angle marked 55°, and the missing angle — find the missing one

Predict each answer before we check it, and say the fact out loud.