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Angles in Polygons

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Sums of Interior Angles TriangleQuadrilateralPentagon Heptagon Octagon Hexagon = 2 triangles = 3 triangles = 4 triangles = 5 triangles= 6 triangles

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Convex Polygon # of Sides# of Triangles Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon n n – (n – 2)

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Find the measure of the missing angle in the figure below x x = quadrilateral x = x = 55

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m 1 = (5x - 5) (4x + 15) (8x - 10) pentagon 5x x x =540 17x + 200= x = 340 x = (20) - 5 = 95 Find m 1.

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Exterior Angles Interior Angles

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Sum of Interior Angles = Sum of Interior & Exterior Angles = Sum of Exterior Angles = = Sums of Exterior Angles 1803 = 540

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180 Sum of Interior Angles = Sum of Interior & Exterior Angles = Sum of Exterior Angles = = Sums of Exterior Angles 1804 = 720

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Sum of Exterior Angles 180 Sum of Interior Angles = Sum of Interior & Exterior Angles = Sum of Exterior Angles = = ° 1805 = 900

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Sum of Exterior Angles Sum of Interior Angles = Sum of Interior & Exterior Angles = Sum of Exterior Angles = = ° 1806 = 1080

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Sums of Exterior Angles Polygon# of Sides Interior + Exterior Interior Angles Exterior Angles Triangle3 Quadrilateral4 Pentagon5 Hexagon Sum of Exterior Angles is always 360 !

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Angles of Regular Polygons Sum of the Interior Angles Sum of the Exterior Angles Each Interior Angle n Each Exterior Angle n 180(n – 2) Always 360 ! 180(n – 2) 360

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Find the sum of the measures of the interior angles of a regular dodecagon. 180(n – 2) = 180(12 – 2) n = 12 = 180(10) = 1800 all 12 angles = each angle What is the measure of each angle?

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The sum of the interior angles of a convex polygon is How many sides does the polygon have? 180(n – 2) = n = n = sides 180n – 360 = 1440

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Exterior Angles What is the measure of each exterior angle of a regular hexagon? sides 6 = 60

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The measure of each exterior angle of a regular polygon is 20. How many sides does it have? =18 The measure of each interior angle of a regular polygon is 120. How many sides does it have? = = 60 exterior angle

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Find the sum of the interior angles of a 100-gon! Find the sum of the exterior angles of a 100-gon. Find the measure of each interior angle of a 100-gon. Find the measure of each exterior angle of a 100-gon.

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