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Warm up the ol’ thinker Solve for x:

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HOMEWORK QUESTIONS? Pg 300 1-15

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Ex. 1 Use the regular pentagon to answer the questions. A)Find the sum of the measures of the interior angles. B)Find the measure of ONE interior angle 540° 108°

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Ex. 2 Use a regular 15-gon to answer the questions. A)Find the sum of the measures of the interior angles. B)Find the measure of ONE interior angle 2340° 156°

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Find the measures of one interior angle of the indicated polygon. 1.Regular triangle 2.Regular heptagon 3.Regular dodecagon

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What about the outside? Finding and using the exterior angle measures of polygons

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Class Lab Each of you will have a different polygon A set of exterior angles has been drawn on your polygon (remember – one set is either clockwise or counterclockwise) Also, an arch has been drawn through each exterior angle Cut out these “pieces of pie” and try to fit them together… Can you solve the puzzle?

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1 2 3 4 5 1 3 2 1 3 2 4

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In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 2 3 4 5

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In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2

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1 3 2 4

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Ex. 1 Find the measure of ONE exterior angle of a regular hexagon. 60°

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Ex. 2 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

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Ex. 3 Each exterior angle of a polygon is 18 . How many sides does it have? n = 20

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Find the measures of an interior angle and exterior angle of the indicated polygon. 1.Regular triangle 2.Regular 20-gon 3.Regular nonagon 4.Regular heptagon 5.Regular dodecagon 6.Regular 17-gon

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How many sides does the polygon have? 1.Each interior angle has a measure of 140º 2.Each interior angle has a measure of 175.2º 3.Each exterior angle has a measure of 45º 4.Each exterior angle has a measure of 3º

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Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have? One interior angle A regular dodecagon

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142 o 105 o 140 o 124 o xoxo 88 o Find the value of x:

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64 o 3x o 2x o 110 o 86 o Find the value of x:

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60 o 100 o 8x o 6x o 20 o Find the value of x:

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The measures of the interior angles of a convex octagon are 45x, 40x, 155, 120, 155, 38x, 158, 41x. What is the measure of the smallest interior angle?

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Homework: Pg 301 # 26 - 35

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Interior and Exterior Angles of Polygons

Interior and Exterior Angles of Polygons

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