Angles in polygons

There are 72 NRICH Mathematical resources connected to Angles in polygons
Isosceles Seven
problem
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Isosceles seven

Age
14 to 16
Challenge level
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Is it possible to find the angles in this rather special isosceles triangle?
Triangle or No Triangle?
problem
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Triangle or no triangle?

Age
5 to 7
Challenge level
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Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Name That Triangle!
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Name that triangle!

Age
7 to 11
Challenge level
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Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Polygon Rings
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Polygon rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

Walking round a triangle
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Walking round a triangle

Age
5 to 7
Challenge level
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This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?
Round a hexagon
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Round a hexagon

Age
7 to 11
Challenge level
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This problem shows that the external angles of an irregular hexagon add to a circle.

Making sixty
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Making sixty

Age
14 to 16
Challenge level
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Why does this fold create an angle of sixty degrees?
Cyclic Quadrilaterals
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Cyclic quadrilaterals

Age
11 to 16
Challenge level
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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Triangles and petals
problem
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Triangles and petals

Age
14 to 16
Challenge level
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An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Semi-regular Tessellations
problem
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Semi-regular tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?