Exploring Polygons and Interior Angles: A Guide for Geometry Enthusiasts

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Discover the fascinating world of polygons and their interior angles on 1st October 2024. Unveil the names, characteristics, and angle calculations of various polygons, including triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons. Learn how to find missing angles, classify regular and irregular polygons, and calculate interior angle sums. Engage in interactive exercises to enhance your geometric knowledge and prepare for an insightful learning experience.

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1 October, 2024 Be Ready 2) Find the missing angle ? 1) Write down the name of following polygons 3) Find the missing angle ? 4) What is the name of the polygon with seven sides?

1 October, 2024 Be Ready 2) Find the missing angle ? 1) Write down the name of following polygons C=180-(38+85) C=57 Triangle 3) Find the missing angle ? Hexagon Square ? = ??? (?? + ??) ? = ?? Pentagon 4) What is the name of the polygon with seven sides? ???????? Octagon

1 October, 2024 Vocabulary check A polygon is a two-dimensional shape with straight sides. Polygon: A polygon is regular when all angles are equal and all sides are equal. Regular: Irregular Polygons

1 October, 2024 Interior Angle Sum of Polygons Name of polygon Number of sides Number of triangles inside polygon Sum of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon

1 October, 2024 How many triangles?

1 October, 2024 Name of polygon Number of sides Number of triangles inside polygon Sum of interior angles Triangle 3 1 1 x 1800 1800 Quadrilateral Pentagon Hexagon Heptagon Octagon

1 October, 2024 How many triangles make up a quadrilateral? 180 180 180 180 2 x 180 = 360 Angles in a quadrilateral always add up to 360

1 October, 2024 Name of polygon Number of sides Number of triangles inside polygon Sum of interior angles Triangle 3 1 1 x 1800 2 x 1800 1800 Quadrilateral 3600 4 2 Pentagon Hexagon Heptagon Octagon

1 October, 2024 Find the angle sum of a pentagon by splitting into as few triangles as possible. 3 x 180 = 540 In pairs, do the same with the pentago n, hexagon , heptago n and octagon Make sure you start splitting the polygon up from the same vertex. Angles in a pentagon always add up to 540 180 180 180

1 October, 2024 Name of polygon Number of sides Number of triangles inside polygon Sum of interior angles Triangle 3 1 1 x 1800 2 x 1800 1800 Quadrilateral 3600 4 2 Pentagon 3 x 1800 5400 5 3 Hexagon 4 x 1800 7200 6 4 Heptagon 5 x 1800 6 x 1800 9000 1080 0 7 8 5 6 Octagon

1 October, 2024 Interior Angle Sum of Polygons So far Interior angle sum of polygons Triangle Quadrilateral Pentagon Hexagon 1 triangle 2 triangles 3 triangles 4 triangles Can you spot the connection between the number of sides and the sum of the interior angles? Sum of interior angles 180 1 180 2 180 3 180 4 Sides Triangles = = = 180 360 540 720 = 3 4 5 6 1 2 3 4 Sum of interior angles 180 2 number of sides (n) What is the interior angle sum of an n-sided shape? n 2 n

1 October, 2024 Interior Angle Sum of Polygons Find the missing angle Step 1: Find the interior angle sum of pentagon Interior angle sum of a pentagon = (5 - 2) x 180 = 3 x 180 = 540 Step 2: Interior angle sum total of other angles Missing angle x = 540 (68 + 121 + 103 + 85) = 540 - 377 = 163 Sum of interior angles in n-sided polygon = (n 2) 180 Where n is the number of sides

1 October, 2024 Your turn 1. Find the interior angle sum in a 12 sided polygon. 2. a) Find the missing angles b) c) Hint: First, find the interior angle sum. Sum of interior angles in n-sided polygon = (n 2) 180 Where n is the number of sides