(round to nearest tenth) Mon, 2/3 SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda Warm-up (10 min) Review HW (20 min) New notes / exit slip (5 – 15 min) Warm-Up: What is 80% of 90% of 10? What is 20% of 15% of 100? What is 25% of 70% of 150? (round to nearest tenth) HW: Read Pgs 353-355 Do Pg. 356 #1-#3 Quiz Thursday! 1

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

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

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

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

Summary Be VERY specific! Sum of interior angles of a triangle = 1800 Exterior angle = Sum of interior angles in triangle

What is 40% of 5/2? What is 65% of ¾? What is 80% of 7/12? Warm-Up: Tues, 2/4 SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda Warm-up / HW Check (10 min) New notes / practice problems (40 min) Warm-Up: What is 40% of 5/2? What is 65% of ¾? What is 80% of 7/12? Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL Quiz Thursday! 8

Chapter 6.1 Polygon Angle – Sum

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

Polygons are named by number of sides Most Common Polygons Polygons are named by number of sides Number of Sides Polygon Triangle 3 4 Quadrilateral Pentagon 5 Hexagon 6 Heptagon 7 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

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

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

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

Warm-Up: Pg. 356 #1 – #3, Pg. 356 #7 – #25 ALL Wed, 2/5 SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda Warm-up (10 min) Notes / practice problems (40 min) Warm-Up: Al is paid 35% as much as Franklin. If Franklin is paid $24.00 per hour, how much is Al paid per hour? 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! 15

Sum of interior angles of a polygon # of sides (n) # of triangles Sum of interior angles of a polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 3 1 180° 4 2 2 · 180 = 360° 5 3 3 · 180 = 540° 4 4 · 180 = 720° 6 7 5 5 · 180 = 900° 8 6 6 · 180 = 1080° n n – 2 (n – 2) · 180°

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

Fri, 2/6 SWBAT… find the sum of the measures of interior and exterior angles of a polygon. Agenda Warm-up (10 min) Notes / practice problems (40 min) Warm-Up: 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? Roman bought a shirt for $11.25. 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 18

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

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°

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 = Sum (n – 2)180 = 3600 180n – 360 = 3600 + 360 + 360 180n = 3960 180 180 n = 22 sides

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 = Sum (n – 2)180 = 2340 180n – 360 = 2340 + 360 + 360 180n = 2,700 180 180 n = 15 sides

Ex: Solve for x x = 27 Sum = (n – 2)180 4x – 2 108 82 2x + 10 6 6 x = 27

Ex. Find the values of the variables and the measures of the angles. 1300 900 1150

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

Ex: What is the measure of each or one interior angle in a regular octagon? (8 – 2)180 / 8 1350

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

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

Ex. Find the exterior angle sum of a decagon.

Ex: Find the value of x Sum of exterior angles is 360° (4x – 12) + 60+ (3x + 13) + 65 + 54+ 68 = 360 7x + 248 = 360 – 248 – 248 7x = 112 7 7 x = 12 (4x – 12)⁰ 68⁰ 60⁰ 54⁰ (3x + 13)⁰ 65⁰

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