Angle facts

The Maths Habit

1 Work out 180 − 130

50

2 Work out 60 + 70

130

3 Work out 360 − 250

110

Angle A gets bigger. What happens to angle B?

ABBefore
→
ABAfter

B gets smaller. Together they still make a straight line.

Angle
The amount of turn between two lines that meet.
Degrees
The units we measure angles in. We write °.
Right angle
A quarter turn. It is 90°. We mark it with a square.
Full turn
Turning all the way round. It is 360°.

Angles on a straight line add up to 180°.

1Total180 or 360°
2Knownangle+angle=
3xtotal−known=°
  1. Pick the total.A straight line is a half turn.
  2. Add the angles you know.
  3. Take them away from the total.What is left is x.

Find the size of angle x.

40°x60°
1Total180°
2Known40+60=100
3x180−100=80°

Find the size of angle x.

x130°
1Total180°
2Known130
3x180−130=50°

Find the size of angle x.

40°x60°
1Total180°
2Known40+60=100
3x180−100=80°

Find the size of angle x.

x110°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known110
3x180−110=70°

Find the size of angle x.

40°x60°
1Total180°
2Known40+60=100
3x180−100=80°

Find the size of angle x.

70°x50°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known70+50=120
3x180−120=60°

Find the size of angle x.

40°x60°
1Total180°
2Known40+60=100
3x180−100=80°

Find the size of angle x.

35°x105°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known35+105=140
3x180−140=40°

Find the size of each angle x.

1x100°
1Total180°
2Known100
3x180−100=80°
265°x45°
1Total180°
2Known65+45=110
3x180−110=70°
3x30°95°
1Total180°
2Known30+95=125
3x180−125=55°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known

Do the angles add up to 180° or 360°?

A360°
B180°
C360°

Angles around a point add up to 360°.

1Total180 or 360°
2Knownangle+angle=
3xtotal−known=°
  1. Pick the total.All the way round is a full turn.
  2. Add the angles you know.
  3. Take them away from the total.What is left is x.

Find the size of angle x.

140°100°x
1Total360°
2Known140+100=240
3x360−240=120°

Find the size of angle x.

160°x120°
1Total360°
2Known160+120=280
3x360−280=80°

Find the size of angle x.

140°100°x
1Total360°
2Known140+100=240
3x360−240=120°

Find the size of angle x.

150°x100°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total360°
2Known150+100=250
3x360−250=110°

Find the size of angle x.

140°100°x
1Total360°
2Known140+100=240
3x360−240=120°

Find the size of angle x.

95°80°x70°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total360°
2Known95+80+70=245
3x360−245=115°

Find the size of angle x.

140°100°x
1Total360°
2Known140+100=240
3x360−240=120°

Find the size of angle x.

x165°110°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total360°
2Known165+110=275
3x360−275=85°

Find the size of each angle x.

1120°130°x
1Total360°
2Known120+130=250
3x360−250=110°
2105°x140°
1Total360°
2Known105+140=245
3x360−245=115°
380°95°100°x
1Total360°
2Known80+95+100=275
3x360−275=85°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known

Angles in a triangle add up to 180°.

  1. Tear the three corners off a triangle.
  2. Put them together, points touching.They make a straight line: 180°.
  3. Use the same frame.Total, known, x.

Find the size of angle x.

70°60°x
1Total180°
2Known70+60=130
3x180−130=50°

Find the size of angle x.

80°40°x
1Total180°
2Known80+40=120
3x180−120=60°

Find the size of angle x.

70°60°x
1Total180°
2Known70+60=130
3x180−130=50°

Find the size of angle x.

50°30°x
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known50+30=80
3x180−80=100°

Find the size of angle x.

70°60°x
1Total180°
2Known70+60=130
3x180−130=50°

Find the size of angle x.

65°75°x
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known65+75=140
3x180−140=40°

Find the size of angle x.

70°60°x
1Total180°
2Known70+60=130
3x180−130=50°

Find the size of angle x.

100°x35°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known
1Total180°
2Known100+35=135
3x180−135=45°

Find the size of each angle x.

165°55°x
1Total180°
2Known65+55=120
3x180−120=60°
2x70°45°
1Total180°
2Known70+45=115
3x180−115=65°
3110°30°x
1Total180°
2Known110+30=140
3x180−140=40°
180°360°180°
1 Total 180° or 360°2 Known add them3 x total − known

Is x right? Thumbs up or thumbs down.

Ax125°x = 55°Right
B60°x70°x = 50°Wrong: 230°
C70°45°xx = 65°Right
D40°x60°x = 260°Wrong: 80°

Angle facts worksheet, page 1

Angle facts worksheet, page 2

Answer sheet

  1. Two straight lines cross. One of the four angles is 50°. Find the other three angles.

    130°, 50°, 130°

  2. Three equal angles fit around a point. How big is each one?

    120°

  3. Two equal angles make a straight line. How big is each one?

    90° (a right angle)

  1. Find the size of angle x. 1Total180°2Known45+75=1203x180−120=60°

    60°
    45°x75°

  2. Find the size of angle x. 1Total360°2Known135+125=2603x360−260=100°

    100°
    135°x125°

  3. Find the size of angle x.

    x = 75°
    65°40°x
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