Angles on a Line and at a Point
Identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning.
Read this first
Angles on a straight line add to 180. Angles all the way round add to 360.
If one angle is 70, the one beside it must be 110.
Words you need
- Straight angle
- A half turn. It is 180 degrees.
- Revolution
- A full turn. It is 360 degrees.
- Vertically opposite
- The angles facing each other when two lines cross.
Worked example
e.g. Two angles sit on a straight line. One is 70 degrees. Find the other.
- Angles on a straight line add to 180.
- So the two angles must total 180.
- Take away the one you know. 180 - 70 = 110.
- The other angle is 110 degrees.
Always say the reason. Write angles on a straight line beside your answer.
Practice
The pictures fade as you go. By the last few you are on your own.
1One angle on a line is 40. Find the other.with a picture
Answer140 degrees.
2Two lines cross. One angle is 65. Find the one opposite it.with a picture
Answer65 degrees. They are vertically opposite.
3Three angles at a point are 120, 150 and x. Find x.with a hint
Need a hint?
They add to 360.
Answer90.
4Two angles on a line are x and 2x. Find x.with a hint
Need a hint?
3x makes 180.
Answer60.
5Four equal angles meet at a point. How big is each?on your own
Answer90 degrees.
6An angle on a line is 90. What is the other?on your own
Answer90 degrees.
7Why are vertically opposite angles equal?on your own
AnswerEach shares a straight line with the same angle.
Think about it
1
Why do angles at a point add to 360?
One good answerThey make one full turn.
2
How does a straight line relate to a full turn?
One good answerA straight line is half a turn, so half of 360.
Common mistakes
Guessing from how the picture looks.
Diagrams are not to scale. Use the rule.
Forgetting to give a reason.
The reason is worth as much as the number.