Year 6: Angles on a line, at a point and opposite
Part of the Year 6 angles, shapes and circles chapter. Chapter overview · whole chapter on one page
Angles on a line, at a point and opposite
An angle is measured in degrees. Three facts help you find a missing angle.
On a straight line the angles add up to 180°, which is half a turn.
At a point the angles add up to 360°, which is a full turn.
When two straight lines cross, the angles that face each other are called vertically opposite angles. They are equal. The angles next to each other around a crossing add up to 180°.
Always name the fact you used, and then show the sum you did.
Key ideas
- Angles on a straight line add up to 180°.
- Angles at a point add up to 360°.
- Vertically opposite angles are equal.
- Angles next to each other on a straight line make 180° together.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a straight line.
- Remember the total for a straight line. Angles on a straight line add up to 180 degrees (a half turn).Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.37° = 37°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 37 = 143
- Write the answer. The missing angle is 143 degrees.143
Check. 143 + 37 = 180, so the angles add up correctly. ✓
Watch out. Use 180 for a straight line, not 360. The angles at a point add up to 360.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for angles at a point.
- Remember the total for angles at a point. Angles around a point add up to 360 degrees (a full turn).Total = 360°
- Add the angles you know. Put them together to see how much of the total is used.90° + 105° + 60° = 255°
- Take the angles you know away from the total. What is left over is the missing angle.360 - 255 = 105
- Write the answer. The missing angle is 105 degrees.105
Check. 105 + 255 = 360, so the angles add up correctly. ✓
Watch out. Use 360 for angles at a point, not 180. A straight line is only 180.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Use the two facts for crossing lines.
- Find c, the vertically opposite angle. Vertically opposite angles are equal.c = 124°
- Find b, the angle next to 124°. The two angles on a straight line add up to 180 degrees.180 - 124 = 56, so b = 56°
- Write the answers. c is the same as the given angle, and b is the rest of the line.124 and 56
Check. 124 + 56 = 180, the straight line. ✓
Watch out. Check your answers with the other fact. The two angles give a straight line.
Exercise 10A Practice: straight lines, points and crossing lines
Non-calculatorKey words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a straight line.
- Remember the total for a straight line. Angles on a straight line add up to 180 degrees (a half turn).Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.63° = 63°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 63 = 117
- Write the answer. The missing angle is 117 degrees.117
Check. 117 + 63 = 180, so the angles add up correctly. ✓
Watch out. Use 180 for a straight line, not 360. The angles at a point add up to 360.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a straight line.
- Remember the total for a straight line. Angles on a straight line add up to 180 degrees (a half turn).Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.36° + 90° = 126°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 126 = 54
- Write the answer. The missing angle is 54 degrees.54
Check. 54 + 126 = 180, so the angles add up correctly. ✓
Watch out. Use 180 for a straight line, not 360. The angles at a point add up to 360.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for angles at a point.
- Remember the total for angles at a point. Angles around a point add up to 360 degrees (a full turn).Total = 360°
- Add the angles you know. Put them together to see how much of the total is used.120° + 95° = 215°
- Take the angles you know away from the total. What is left over is the missing angle.360 - 215 = 145
- Write the answer. The missing angle is 145 degrees.145
Check. 145 + 215 = 360, so the angles add up correctly. ✓
Watch out. Use 360 for angles at a point, not 180. A straight line is only 180.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for angles at a point.
- Remember the total for angles at a point. Angles around a point add up to 360 degrees (a full turn).Total = 360°
- Add the angles you know. Put them together to see how much of the total is used.80° + 75° + 110° = 265°
- Take the angles you know away from the total. What is left over is the missing angle.360 - 265 = 95
- Write the answer. The missing angle is 95 degrees.95
Check. 95 + 265 = 360, so the angles add up correctly. ✓
Watch out. Use 360 for angles at a point, not 180. A straight line is only 180.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Vertically opposite angles are equal, so copy the size of the angle.
- Look at the two straight lines that cross. Angles that face each other at a crossing are called vertically opposite angles.The angle given is 47°
- Use the rule: vertically opposite angles are equal. So the angle opposite is the same size.Opposite angle = 47°
- Write the answer. The angle opposite is the same size as the one given.47
Check. The angle next to it on a straight line is 180 - 47 = 133, and 47 + 133 = 180. ✓
Watch out. Vertically opposite means the angles face each other, not the ones next to each other.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Vertically opposite angles are equal, so copy the size of the angle.
- Look at the two straight lines that cross. Angles that face each other at a crossing are called vertically opposite angles.The angle given is 35°
- Use the rule: vertically opposite angles are equal. So the angle opposite is the same size.Opposite angle = 35°
- Write the answer. The angle opposite is the same size as the one given.35
Check. The angle next to it on a straight line is 180 - 35 = 145, and 35 + 145 = 180. ✓
Watch out. Vertically opposite means the angles face each other, not the ones next to each other.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a straight line.
- Remember the total for a straight line. Angles on a straight line add up to 180 degrees (a half turn).Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.35° = 35°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 35 = 145
- Write the answer. The missing angle is 145 degrees.145
Check. 145 + 35 = 180, so the angles add up correctly. ✓
Watch out. Use 180 for a straight line, not 360. The angles at a point add up to 360.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Add the angles you know, then take them away from the total for a straight line.
- Remember the total for a straight line. Angles on a straight line add up to 180 degrees (a half turn).Total = 180°
- Add the angles you know. Put them together to see how much of the total is used.40° + 65° = 105°
- Take the angles you know away from the total. What is left over is the missing angle.180 - 105 = 75
- Write the answer. The missing angle is 75 degrees.75
Check. 75 + 105 = 180, so the angles add up correctly. ✓
Watch out. Use 180 for a straight line, not 360. The angles at a point add up to 360.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Share the full turn equally between the angles.
- Remember: the angles at a point add up to 360 degrees. That is a full turn.360 degrees
- Share 360 equally between the angles. All the angles are the same size, so divide by how many there are.360 ÷ 5 = 72
- Write the answer. Each angle is this many degrees.72
Check. 72 × 5 = 360. ✓
Watch out. Use 360 for a full turn around a point. Do not use 180.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Share the total into equal parts using the ratio, then work out each angle.
- Add the parts of the ratio. Each part of the ratio is one share of the total.2 : 3: 5 parts in all
- Find the size of one part. Share the total of 180 degrees into 5 equal parts.180 ÷ 5 = 36
- Work out each angle. Multiply each ratio number by the size of one part.2 × 36 = 72, 3 × 36 = 108
- Write the answer. The largest angle is 108 degrees.108
Check. The angles add up to 72 + 108 = 180. ✓
Watch out. Share the total by the number of parts, not by the number of angles.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Use the fact that angles at a point add up to 360, not 180.
- Check the rule for a straight line. A straight line makes 180 degrees. That is half a turn.straight line = 180
- Check the rule for a full turn. Angles at a point go all the way round, so they make a full turn.angles at a point = 360
- Compare the two rules. Ali has used the rule for a straight line, but the angles are at a point.180 is not 360, so Ali is wrong
- Write the answer. Ali is not right.No
Check. Four angles at a point could be 90, 90, 90 and 90, which add up to 360. ✓
Watch out. Angles at a point add up to 360. A straight line is only 180.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. The vertically opposite angle is the same size, so it is not the angle next to it.
- Find the vertically opposite angle. Opposite angles at a crossing are equal.opposite angle = 70°
- Find the angle next to 70°. That angle is on a straight line with 70, so it is 180 - 70.180 - 70 = 110°
- Write the answer. Sam has used the angle next to it, not the opposite one.No
Check. 70 + 110 = 180. ✓
Watch out. Vertically opposite angles are equal. Angles next to each other are not.
Key words. An angle is the turn between two lines. Angles are measured in degrees (°). A straight line makes a half turn of 180°. A full turn around a point is 360°.
Method. Set up an equation with the four angles, then solve it.
- Write the four angles as an equation. Angles at a point add up to 360 degrees.x + 2x + 3x + 90 = 360
- Collect the x terms. x + 2x + 3x is 6 lots of x.6x + 90 = 360
- Take 90 from 360. What is left is the 6 lots of x.360 - 90 = 270, so 6x = 270
- Divide by 6 to find x. This gives the size of one x.270 ÷ 6 = 45
- Write the answer. x is 45 degrees.45
Check. 45 + 90 + 135 + 90 = 360, the full turn. ✓
Watch out. Keep the 90 degree angle separate. It is not an x angle.
Watch out
Common mistake: using 180 for angles at a point, or 360 for a straight line. Look at the picture first and decide which total you need.
Exam tip
In the test, write down the fact you used, such as "angles on a straight line add up to 180", before you do the sum.