Angles - points, lines and parallel lines

There are 81 NRICH Mathematical resources connected to Angles - points, lines and parallel lines
Round and round and round
problem
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Round and round and round

Age
11 to 14
Challenge level
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Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?
Which solids can we make?
problem
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Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

How Safe Are You?
problem
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How safe are you?

Age
7 to 11
Challenge level
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How much do you have to turn these dials by in order to unlock the safes?
Triangles in circles
problem
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Triangles in circles

Age
11 to 14
Challenge level
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Can you find triangles on a 9-point circle? Can you work out their angles?

Six Places to Visit
problem
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Six places to visit

Age
7 to 11
Challenge level
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Can you describe the journey to each of the six places on these maps? How would you turn at each junction?
Angle Trisection
problem
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Angle trisection

Age
14 to 16
Challenge level
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It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Subtended angles
problem
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Subtended angles

Age
11 to 14
Challenge level
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What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
Turning
problem
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Turning

Age
5 to 7
Challenge level
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Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Right angles
problem
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Right angles

Age
11 to 14
Challenge level
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Can you make a right-angled triangle on this peg-board by joining up three points round the edge?