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SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review HW (20 min) 3. New notes / exit slip (5 – 15 min) Warm-Up: 1. What is 80% of 90% of 10? 2. What is 20% of 15% of 100? 3. What is 25% of 70% of 150? (round to nearest tenth) HW: Read Pgs Do Pg. 356 #1-#3 Quiz Thursday! Mon, 2/3

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The sum of the interior measures of the angles of a triangle is 180 degrees. Triangle Sum Theorem

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The measures of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Triangle Exterior Angle Theorem

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Review HW: Page 175: #1 – #21 ALL Page 177: #29 – #32 ALL

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Exit Slip: ½ sheet – Collected 1.) Find the value of x, y, and z? 3.) Find m<1 and m<2. 2.) Find the value of x

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Summary Be VERY specific! 1. Sum of interior angles of a triangle = Exterior angle = Sum of interior angles in triangle

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SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up / HW Check (10 min) 2. New notes / practice problems (40 min) Warm-Up: 1. What is 40% of 5/2? 2. What is 65% of ¾? 3. What is 80% of 7/12? Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL Quiz Thursday! Tues, 2/4

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Chapter 6.1 Polygon Angle – Sum

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Polygon A closed plane figure formed by 3 or more segments that all lie in one plane

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Polygons are named by number of sides Number of SidesPolygon n Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon

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An equilateral polygon: All sides congruent. An equiangular polygon: All angles congruent. A regular polygon: All the sides and angles congruent. Equilateral PolygonEquiangular Polygon Regular Polygon

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Concave If any part of a diagonal contains points in the exterior of the polygon.

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Convex If no diagonal contains points in the exterior. A regular polygon is always convex.

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SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min) 2. Notes / practice problems (40 min) Warm-Up: 1. Al is paid 35% as much as Franklin. If Franklin is paid $24.00 per hour, how much is Al paid per hour? 2. Nancy gets paid $12.00 per hour at her job at the grocery store. Susie is paid 120% as much as Nancy. How much is Susie paid per hour? Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL Quiz Tomorrow! Wed, 2/5

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Polygon# of sides (n) # of trianglesSum of interior angles of a polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon n n – ° 2 · 180 = 360° 3 · 180 = 540° 4 · 180 = 720° 5 · 180 = 900° 6 · 180 = 1080° (n – 2) · 180°

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Ex: What is the measure of angle Y in pentagon TODAY?

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SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda 1. Warm-up (10 min) 2. Notes / practice problems (40 min) Warm-Up: 1. Tomas bought a new book on sale. It cost $17.95 but was on sale for 20% off. How much did the book cost Tomas? 2. Roman bought a shirt for $ He was able to receive a discount on the shirt for 30% off. How much did Roman pay for the shirt? Pg. 421 #5 – 10 Fri, 2/6

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Polygon Angle-Sum Theorem The sum of the measures of the interior angles of an n-gon is: Sum = (n – 2)180 n = the number of sides

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Ex: What is the sum of the measures of the interior angles of an octagon? Sum = (n – 2)180 = (8 – 2)180 = 6 * 180 = 1,080°

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1. Ex: If the sum of the measures of the interior angles of a convex polygon is 3600°, how many sides does the polygon have. (n – 2)180 = n – 360 = n = n = 22 sides (n – 2)180 = Sum

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1. Ex: If the sum of the measures of the interior angles of a convex polygon is 2340°, how many sides does the polygon have. (n – 2)180 = n – 360 = n = 2, n = 15 sides (n – 2)180 = Sum

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4x – x x – 2 + 2x + 10 = (4 – 2)180 6x = 360 6x = x = 27 Ex: Solve for x Sum = (n – 2)180

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Ex. Find the values of the variables and the measures of the angles. x =

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The measure of each interior angle of a regular n-gon is

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Ex: What is the measure of each or one interior angle in a regular octagon? (8 – 2)180 /

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What do you notice about the exterior angles of the polygons below?

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Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

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Ex. Find the exterior angle sum of a decagon.

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54⁰ 68⁰ 65⁰ (3x + 13)⁰ 60⁰ (4x – 12)⁰ Sum of exterior angles is 360° (4x – 12) (3x + 13) = 360 7x = 360 – 248 – 248 7x = x = 12 Ex: Find the value of x

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Ex: What is the measure of angle 1 in the regular octagon?

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