Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level35. Regular Polygons1. a) Calculate the value of the angle x in this regular octagon.b) What is the size of angle y?c) Calculate the size of angle z.In each, clearly explain how you arrive at your answer.2. What is the sum of all the exterior angles of a polygon?yz3. Regular hexagons and squares are put together ina row, as shown in the diagram on the right.Calculate the size of the angle marked x. Explainclearly how you arrive at your answer.xx4. A five pointed regular star shape is to be cut froma piece of card. In order to draw it accurately it isnecessary to calculate the angles x and y. Calculatethese angles, explaining clearly how you arrive at theanswers.xy5. What regular shape can be made from a regularhexagon and three regular triangles, all with sidelengths of x centimetres? What will be the length ofone side of the new shape?6. In the regular heptagon shown on the right AB andDC are produced to meet at H.a) Calculate the sizes of angles BCD and BHC, ineach case explaining how you arrive at youranswer.b) Prove that BC is parallel to AD.7. Three regular polygons fit together around a point.One is a triangle and one is an octagon. Calculate thenumber of sides the third shape has.GAFBEHCD