A regular polygon is a polygon where all the sides and included angles are equal. Examples include the equilateral triangle and the square.
REGULAR POLYGONS internal and external angles
For this lesson each student will need a protractor, ruler, paper, pencil. The teacher will need to have printed and laminated and cut the regular shapes. (It is best to use coloured paper, but not essential.) He should also print out enough worksheets for each student.
Click on the images below. Print on coloured paper and laminate the pages.
1) Hand out laminated shapes. Say what a regular polygon means. ( On the board write S3 = triangle, S4 = square, S5 = pentagon, S6= hexagon, S7 = heptagon, S8 = octagon, S9 = nonagon, S10 = decagon, S11 = hendecagon, S12 = dodecagon.)
2) With protractors, try to measure the internal angles and external angles of each shape. Write down your results on the worksheet.
3) Compare the results on the board. Explain how the internal and external angle should add up to 180. Show how 360 shared by the number of sides equals the external angle. For instance the external angle of a regular octagon = 360 shared by 8 = 45 degrees. So the internal angle must be 180 - 45 = 135 degrees.
Extra Work. What is the internal and external angle of a 20 sided regular polygon? 30 sided? 25 sided? (answers 20 sided ext = 18, int = 162, .... 30 sided ext =12, internal = 168, ..... 25 sided internal 14.4, ext =165.6)
4) What are the correct answers to the internal and external angles, worked out by Maths? For instance heptagon has seven sides. External angle 360 shared by 7 = 51.4, so the internal angle should be 180 - 51.4 = 128.6 degs.