When two straight lines cross they make an X with four angles. The angles across from each other are vertically opposite, and they are equal. Angles next to each other sit on a straight line, so they add up to 180°. First decide which kind of pair you have. With more lines, carry a known angle across to its opposite, then use a straight line.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- vertically opposite
- across from each other where two lines cross
- adjacent
- next to each other, sharing an arm
Worked examples
Two lines cross. One angle is 70°. Find the angle opposite it.
- 1.Vertically opposite angles are equal.
- 2.The angle is 70°.
= 70
Two lines cross. One angle is 70°. Find the angle next to it.
- 1.Next-door angles make a straight line: 180°.
- 2.180 − 70 = 110.
= 110
Three lines cross. 50° and 70° are labelled; ? is on a straight line with the 50° angle and the angle opposite the 70°. Find ?.
- 1.The angle opposite 70° is also 70°.
- 2.50 + 70 = 120, and 180 − 120 = 60.
= 60
For parents
Method: Cross two pencils and open them: the opposite gaps change together.
What to say: Is the unknown angle across from the one you know, or next to it?
Common mistakes:
- Measures or estimates the angle from the picture, although the diagram is not drawn to scale.
- Thinks vertically opposite angles add up to 180° instead of being equal.
- Thinks the angle next to the labelled one is equal to it, mixing up 'next to' with 'opposite'.
- Takes the known angles away from 360° although only part of the turn is involved.
- With three lines, subtracts only the angle on the same line and forgets to carry the other angle across first.