step 1 of 7
You already know a full turn is 360 degrees, like spinning all the way around and facing the start again. A round pie is cut into three slices that all meet at the center point.
How many degrees do all three slices add up to?
به انگلیسی
Angle Sum Rules
Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles
What a learner can do afterwards
- State that two angles on a straight line add to 180°
- Explain that four right angles at a point make 360°
- Identify 270° as three right angles
1 · Read
Think of a book lying open flat on a table, its two covers forming one straight line. When two angles sit side by side on a straight line like that, they always add up to 180°. A straight line is half of a full turn, so its angles share that half.
When angles meet at one point and go all the way around it, they add up to 360°, a whole turn. Four right angles fit exactly around a single point, because 90° + 90° + 90° + 90° = 360°.
When two straight lines cross, they make two pairs of angles across from each other. Each pair is called vertically opposite angles, and the two angles in a pair are always equal.
Try it together
Three angles meet at a point: 150°, 100°, and one more angle. All the angles at a point add up to 360°, so add the two known angles first: 150° + 100° = 250°. Then subtract from 360°: 360° − 250° = 110°. The missing angle is 110°.
Good to know
After you find a missing angle, add all the angles back together to check. On a straight line the total should be 180°. Around a point it should be 360°.
Straight line angles add to 180°, angles around a point add to 360°, and vertically opposite angles match.
More to read
Angles around a point
Imagine you stand in one spot and spin all the way around, back to where you started. That spin is one full turn, and it measures 360 degrees. When several angles meet at a single point, they share that full turn, so they must add up to 360 degrees. Example: three angles meet at a point. They measure 100 degrees, 120 degrees, and x degrees. Step one: add the angles you know. 100 plus 120 is 220. Step two: take that away from 360, because the full turn is 360. 360 take away 220 is 140. So x is 140 degrees. Try saying it in words: the three angles together make one whole turn. If you know some of the pieces, add them up and subtract from 360 to find the missing piece.
Angles inside right angles and straight lines
A big angle can be split into smaller angles, and the smaller angles must add up to the whole. A right angle is the square corner angle, and it always measures 90 degrees. If a right angle is split into 55 degrees and a missing angle, you know 55 plus the missing angle equals 90, so the missing angle is 35 degrees. A straight line is even bigger. Angles on a straight line add up to 180 degrees. If one angle on a straight line is 110 degrees, the other must be 180 take away 110, which is 70 degrees. Think of it like a puzzle. The pieces must fit together exactly to make the whole angle. When you see a missing angle, ask yourself: does the whole equal 90 or 180? Then subtract what you know.
Vertical angles: the matching pair
When two straight lines cross each other, they make four angles. The angles that sit opposite each other are called vertical angles, and they are always equal. Picture an X. The top and bottom openings match each other, and the left and right openings match each other too. So if one angle in the X is 60 degrees, the angle straight across from it is also 60 degrees. You do not even need to measure it. The angles next to each other are different. They sit together on a straight line, so they add up to 180 degrees. That means if one angle is 60, its neighbor is 120, the one across is 60 again, and the last one is 120. With just one number, you can find all four angles in the X.
Explore more
2 · Watch
به انگلیسی3 · Play
به انگلیسی
Take it off screen
Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.