# Exterior angle number of sides test your

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Exterior angle Number of sides Test Your Understanding: a. A regular polygon has an exterior angle of . How many sides does it have? b. A regular polygon has an interior angle of . How many sides does it have? c. A regular polygon has 15 sides. What is each interior angle?
33 d. The diagram on the left shows a regular hexagon and a regular octagon. Calculate the angle 119. Use geometric language appropriately and recognise and name pentagons, hexagons, heptagons, octagons and decagons Simply a case of memorisation. Num sides Name Num sides Name 4 Quadrilateral 8 Octagon 5 Pentagon 9 Nonagon 6 Hexagon 10 Decagon 7 Heptagon (not ‘septagon’!) 120. Understand tessellations of regular and irregular polygons and combinations of polygons. Explain why some shapes tessellate when other shapes do not. . Shapes tessellate (whether multiple copies of the same shape or different shapes) when the interior angles joining at a point sum to . For example, a hexagon tessellates with itself as we can join 3 hexagons each with interior angle , whereas a pentagon does not tessellate because its interior angle of is not a factor of 360. More complicated problems might require to you to find the interior angle first before calculating the number of sides e.g. “ Two copies of a regular polygon and a square tessellate as pictured. Prove that is an octagon.” At any point in the diagram, there is one square and two copies of . Thus interior angle of is . Exterior angle of Number of sides of , thus is an octagon. Test Your Understanding: A pattern is made up of two tiles, A and B, as pictured on the right. Both tiles are regular polygons. Work out how many sides Tile A has. 2D and 3D Shapes 121. Use 2-D representations of 3-D shapes. Use isometric grids. Draw nets and show how they fold to make a 3-D solid An isometric grid is one which consists of equilateral triangles, inside of the usual squares. 122. Understand and draw front and side elevations and plans of shapes made from simple solids. Given the front and side elevations and the plan of a solid, draw a sketch of the 3-D solid Recall that the plan is the view from the top, the front elevation is the horizontal view from the designated ‘front’ (which will be indicated), and the side elevation the horizontal view from the side. Example: Consider the following shapes sketched isometrically: Then the plan, front elevation and side elevation are as follows. Ensure you correctly count the number of squares! Test Your Understanding: A cuboid is as pictured. On a square grid, draw the plan, front elevation and side elevation.
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