Mod 15.1: Interior and Exterior Angles

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Module 15: Lesson 1 Interior & Exterior Angles
Presentation transcript:

Mod 15.1: Interior and Exterior Angles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? CASS: G-CO.10 Prove theorems about triangles. MP.8 Patterns

EXPLORE 1 Exploring Interior Angles in TrianglesPLORE 1

EXPLORE 1 4 5 Alternate Interior Angles Theorem 1 3 Substitution Property of Equality

EXPLORE 2 Exploring Interior Angles in Polygons1

EXPLORE 2 Exploring Interior Angles in Polygons1

Exploring Interior Angles in Polygons1 EXPLORE 2 Exploring Interior Angles in Polygons1 Reflect

Polygon Angle Sum Theorem The sum of the measures of the interior angles of a convex polygon with n sides is EXPLAIN 1 Given a nonagon, find the sum of measures of its interior angles. Then find the measure of each angle. So the total of the interior angle measures is 1260⁰. Each angle measures 140⁰.

Polygon Angle Sum Theorem Your Turn: On WS 15.1, complete # 1-8c 8b) 6 sides 8c) 52 sides 1260º; 140º 540º; 108º 1800º; 150º 900º; 128.6º 360º; 90º 2520º; 157.5º 1440º; 144º 720º; 120º 78º 26º 86º 154º 6 9 11 100º 65º

EXAMPLE 1A

EXAMPLE 1B

Your Turn Exploring Interior Angles in Polygons1

Exploring Interior Angles in Polygons1 Your Turn Exploring Interior Angles in Polygons1 n = 6 Sum = (6 - 2)180° = (4)180° = 720° b + 2b + 69 + 108 + 135 + 204 = 720 b = 68 2b = 136 The two unknown angle measures are 68° and 136°. n = 4 Sum = (4 - 2)180° = 2(180°) = 360° 89 + 80 + 104 + x = 360 x = 87 The unknown angle measure is 87°.

EXPLAIN 2 50 + 70 + x = 180 120 + x = 180 x = 60 exterior angles B C exterior angles 50 + 70 + x = 180 70º 50º 120 + x = 180 (x)º (y)º x = 60 x + y = 180 60 + y = 180 y = 120

Exterior Angle Theorem B The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. 2 1 3 A C 1 + 2 = 3

EXAMPLE 2 Triangle Sum Theorem 180˚ 3 4 m∠ 1 + m∠ 2 = m∠ 4

Exterior Angle Theorem Your Turn: WS 15.1 problems # 9 - 12 Answers: 9) 78° 10) 26° 11) 86° 12) 154°

EXAMPLE 3 145 = 2z + 5z - 2 x = 50 145 = 7z - 2 z = 21 m∠PRS = 142° m∠B = (5z - 2)° = (5(21) - 2)° = (105 - 2)° = 103°

15x + 6 = 72 + (3x + 6) 15x + 6 = 78 + 3x –3x – 6 – 6 – 3x 12x = 72 EXPLAIN 3 15x + 6 = 72 + (3x + 6) 15x + 6 = 78 + 3x –3x – 6 – 6 – 3x 12x = 72 12 12 x = 6

Exterior Angle Theorem Your Turn: WS 15.1 complete # 13 - 18 6 9 11 100º 65º

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