Geometry and measures

Lines and angles

Use complementary, supplementary, vertically opposite and parallel-line angle facts.

Most angle questions are really about what a set of angles has to add up to. Angles that make a right angle come to 90°, angles side by side on a straight line come to 180°, and angles that fill the space round a point come to 360°. Work out which of those three a question is about, and the rest is subtraction.

Complementary and supplementary

Complementary angles add up to 90°; supplementary angles add up to 180°. The two words are easy to swap by mistake, and C comes before S in the alphabet just as 90 comes before 180 — a small thing, but it settles it every time.

Have a play

Two straight lines cross, and only one of the four angles they make has been given to you. Find out how big each of the others is.

Tap any part of the picture.

Worked example

Two straight lines cross. One of the four angles is 70°. How big are the other three?

  1. The angle next to it shares a straight line with it, so it is 180° - 70° = 110°.

    Two angles side by side on a straight line are supplementary, however slanted the picture looks.

Three facts that need the lines to be parallel

When a straight line crosses two parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior angles add up to 180°. All three depend on the two lines genuinely being parallel. If they are not, none of the three holds, and a drawing on its own will not tell you which case you are in — the question has to say so.

Try it together

Now one together. Two angles sit side by side on a straight line, and the larger one is 30° bigger than the smaller.

There is nothing here to measure, so start from what the two angles must come to and work backwards.

    1.What do the two angles add up to, in degrees?

    Have a go

    Have a go on your own. Two parallel lines are cut by a transversal, and one co-interior angle is 118°. How big is the other, in degrees?

    Hint: Co-interior angles are the pair that make 180° between them.

    Ready to practise?

    Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.

    Print a worksheet