Polygons – Measurements of Angles

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Presentation transcript:

Polygons – Measurements of Angles State the Name for each Polygon described 3 Sides : 4 Sides : 5 Sides : 6 Sides : 7 Sides : 8 Sides : 9 Sides : 10 Sides : n Sides : Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-gon

Finding the Sum of interior angles of any polygon Shape Sum of interior angles Triangle: 180° Quadrilateral : Pentagon Hexagon 2 triangles = 360° 3 triangles = 540° 4 triangles = 720 ° n-gon = 180(n - 2) Where n = number of sides

For any polygon – To find the sum of the interior angles use the formula: Sum of interior angles = 180(n – 2) Where n = # of sides Ex. Find the sum of the interior angles for the following a) Octagon b) 13-gon 180(n – 2) 180 (8 – 2) 180(6) 1080 180(n – 2) 180(13 – 2) 180(11) 1280

Ex. Find the value of x. 180(n – 2) 180(5 – 2) 180(3) 540 x + 89 + 106 + 107 + 116 = 540 x + 418 = 540 x + 418 – 418 = 540 – 418 x = 122

Regular Polygon : All angles are equal Ex. Find the measure of an interior angle of a regular hexagon. 180(n – 2) 180(6 –2) 180(4) 720 720 6 120 One interior angle of regular hexagon is 120

Find the value of x. 85 57 112 x