Here is the first lesson, Florence. It is a gentle one — read at your own pace. Nothing here is timed, and nothing is written to catch you out.
It works in small steps. When a question appears, choose an answer by tapping it. If it isn't right, nothing happens except a quiet nudge — you simply try again, and there is always a “show me how” if you would like to see it worked through.
By the end you will be able to find a missing angle on a straight line, a missing angle around a point, and the angles made when two lines cross. They turn up constantly, so they are good ones to have firmly. Tap Continue when you are ready.
Picture standing at a point on a straight line, looking along it one way. To end up looking the other way, you turn halfway around — and a half turn is 180°.
So any angles that meet at a point on a straight line must, together, fill that half turn. They add up to 180°. If you know all of them but one, you find the missing angle by subtracting the rest from 180°.
All the angles along a straight line add up to 180°. There are three of them here, so the three together make 180°.
43° + 90° + x = 180°
Add up the two you already know, then take that total away from 180°.
43° + 90° = 133°, and 180° − 133° = 47°
Angles on a straight line add up to 180°.
One angle is 110°, so the other is 180° − 110° = 70°.
The three angles add up to 180°.
Add the two you know: 55° + 75° = 130°.
Then 180° − 130° = 50°.
Angles on a straight line add up to 180°.
Add the two you know: 90° + 34° = 124°.
Then 180° − 124° = 56°.
The first idea was half a turn. The second is the whole turn.
Picture turning all the way around until you face your starting direction again. A full turn is 360°. So angles that meet at a single point and fill the whole space around it must add up to 360° — and again, if you know all but one, you subtract the rest from 360°.
Angles around a point add up to 360°, so the three here make 360° together.
150° + 90° + x = 360°
Add the two you know, then take the total away from 360°.
150° + 90° = 240°, and 360° − 240° = 120°
Angles around a point add up to 360°.
One angle is 215°, so the other is 360° − 215° = 145°.
The three angles add up to 360°.
Add the two you know: 120° + 95° = 215°.
Then 360° − 215° = 145°.
Angles around a point add up to 360°.
Add the three you know: 90° + 90° + 100° = 280°.
Then 360° − 280° = 80°.
When two straight lines cross, they make four angles at the point where they meet. The two angles that sit directly opposite each other — across the crossing — are always equal. They are called vertically opposite angles.
It follows from the very first idea. Each angle and the one beside it lie together on a straight line, so they add to 180° — and that forces the two opposite angles to match.
Angle x is straight across the crossing from the 65° angle — it is vertically opposite, and vertically opposite angles are equal.
x = 65°
Angle y sits next to the 65° angle, and the two of them lie together on a straight line — so they add to 180°.
y = 180° − 65° = 115°
When two lines cross, the angles opposite each other are equal.
So the angle vertically opposite 125° is also 125°.
The angle next to it lies on a straight line with the 40° angle.
Angles on a straight line add up to 180°, so it is 180° − 40° = 140°.
This last part takes two steps, and uses the first two ideas. Here is the first.
Angles on a straight line add up to 180°.
So a = 180° − 130° = 50°.
You worked out that a = 50°. Now carry it into the second step.
Angles around a point add up to 360°.
Add what you know: 50° + 90° = 140°.
Then b = 360° − 140° = 220°.
That's the lesson done, Florence.
You came back to maths after a break, and you did it on your own — reading each part, working through it, thinking it out yourself. Today you learned three solid facts: angles on a straight line make 180°, angles around a point make 360°, and where two lines cross, the angles opposite each other are equal. They're yours now, and you'll use them often.
Sitting down to this by yourself takes something. You did that today. The next lesson will be here whenever you're ready for it.
You can close this page now — or step back through any part you'd like to see again.