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Whiteboardmaths.com © 2004 All rights reserved

Interior Angles of Polygons Quadrilateral Pentagon Hexagon Heptagon/ Septagon 180 o 4 sides 5 sides 6 sides7 sides 180 o 2 x 180 o = 360 o 2 3 x 180 o = 540 o 3 4 x 180 o = 720 o 4 5 x 180 o = 900 o 5 Find the connection between the number of sides and the number of triangles. The sum of the interior angles of an” n” sided polygon is? (n – 2) triangles = (n – 2)180 o

Interior Angles of Polygons Septagon/HeptagonDecagonHendecagon Dodecagon HexadecagonIcosagon 7 sides10 sides11 sides 12 sides 16 sides20 sides 9 sides Nonagon 900 o /128.6 o 1260 o /140 o 1440 o /144 o 1620 o /147.3 o 1800 o /150 o 2520 o /157.5 o 3240 o /162 o Calculate the angle sum and interior angle of each of these regular polygons to 1 dp

2 x 180 o = 360 o 360 – 245 = 115 o 3 x 180 o = 540 o 540 – 395 = 145 o Interior Angles of Polygons y 117 o 121 o 100 o 125 o 140 o z 133 o 137 o 138 o 125 o 105 o Find the unknown angles below. 75 o 100 o 70 o x 115 o 110 o 75 o Diagrams not drawn accurately. w 95 o 4 x 180 o = 720 o 720 – 603 = 117 o 5 x 180 o = 900 o 900 – 776 = 124 o

2 x 180 o = 360 o 360 – 240 = 120 o 3 x 180 o = 540 o 540 – 418 = 122 o Interior Angles of Polygons 5 x 180 o = 900 o 900 – 780 = 120 o 4 x 180 o = 720 o 720 – 595 = 125 o y 120 o 115 o 85 o 120 o 155 o Now try these ones yourself. x 120 o 115 o 95 o 88 o 1 2 Diagrams not drawn accurately. z 155 o 95 o 125 o 165 o 150 o 75 o w 34

Interior Angles of Polygons

7 sides10 sides11 sides 12 sides 16 sides20 sides 9 sides Calculate the angle sum and interior angle of each of these regular polygons to 1 dp

Interior Angles of Polygons y 117 o 121 o 100 o 125 o 140 o z 133 o 137 o 138 o 125 o 105 o Find the unknown angles below. 75 o 100 o 70 o x 115 o 110 o 75 o Diagrams not drawn accurately. w 95 o

Interior Angles of Polygons y 120 o 115 o 85 o 120 o 155 o Now try these ones yourself. x 120 o 115 o 95 o 88 o 1 2 Diagrams not drawn accurately. z 155 o 95 o 125 o 165 o 150 o 75 o w 34