Angles · Usually met around P6
Vertically opposite angles and angles at a point
Opposite angles are equal; side by side make 180°; round a point 360°.
How to do it
Method
Opposite angles are equal; side by side make 180°; round a point 360°
Opposite 50° is 50°; beside it is 130°
Another way
Use the straight lines
180 − 130 = 50
In full
Two straight lines crossing make four angles. The two facing each other across the point are vertically opposite, and vertically opposite angles are equal: if one is 50°, the one across from it is 50° too. Two angles side by side lie on a straight line and make 180°: the angle beside 50° is 180 − 50 = 130°. Angles round a point make 360°; if several unknown angles x are equal, take the known angles from 360, then share out what is left: 360 − 100 − 80 = 180, 180 ÷ 2 = 90, so x = 90°. Another way, which shows why opposite angles are equal: 50 + 130 = 180 on one line, and the angle across + 130 = 180 on the other, so the angle across is 180 − 130 = 50.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Two straight lines cross, making four angles. One is 150°. How many degrees is the angle opposite it?
- A. 300°
- B. 150°
- C. 210°
- D. 30°
Choose the right answer
Show the answer and working
Answer: B. 150°
Vertically opposite angles are equal: 150°.
Example 2
Two straight lines cross. x = □°, y = □°, z = □°
Fill in each box
Show the answer and working
Answer: 75，105，75
x is on a line with 105°: 180 − 105 = 75; y is opposite 105°: 105; z is opposite x: 75.
Example 3
Three straight lines cross at one point. What is the angle marked ? in degrees?
Show the answer and working
Answer: 65°
The angle opposite 80° is also 80°, and it lies on one line with 35° and ?: 180 − 35 − 80 = 65.
Practise it in the game →Angles · Free to start, unlimited questions, no download