Unit 8 Angle Relationships Lesson 4 Exterior Angles

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Unit 8 Angle Relationships Lesson 4 Exterior Angles of Triangles

Unit 8 Angle Relationships Lesson 4 Exterior Angles of Triangles

Lesson 4: Exterior Angles of Triangles Objective: SWBAT find the measures of exterior angles

Lesson 4: Exterior Angles of Triangles Objective: SWBAT find the measures of exterior angles in a triangle. Do Now:

Lesson 4: Exterior Angles of Triangles Exterior Angle – is formed by one side

Lesson 4: Exterior Angles of Triangles Exterior Angle – is formed by one side of the triangle and the extension of the adjacent side. Each exterior angle has 2 remote interior angles that are not adjacent to the exterior angle. Exterior Angle and Remote Interior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Lesson 4: Exterior Angles of Triangles Angle 1 + Angle 2 = Angle 4

Lesson 4: Exterior Angles of Triangles Angle 1 + Angle 2 = Angle 4 Angle 2 + Angle 3 = Angle 5 Angle 1 + Angle 3 = Angle 6 6 2 5 1 3 4

Lesson 4: Exterior Angles of Triangles Example #1: Suppose Angle 1 = 65° and

Lesson 4: Exterior Angles of Triangles Example #1: Suppose Angle 1 = 65° and Angle 2 = 55°, what is the measure of Angle 4? 2 1 3 4

Lesson 4: Exterior Angles of Triangles Example #1: Suppose Angle 1 = 65° and

Lesson 4: Exterior Angles of Triangles Example #1: Suppose Angle 1 = 65° and Angle 2 = 55°, what is the measure of Angle 4? Angle 1 + Angle 2 = Angle 4 65 + 55 = Angle 4 120 = Angle 4 = 120° 2 1 3 4

Lesson 4: Exterior Angles of Triangles Example #2: Suppose Angle 1 = 65° and

Lesson 4: Exterior Angles of Triangles Example #2: Suppose Angle 1 = 65° and Angle 4 = 125°, what is the measure of Angle 3? 4 2 1 3

Lesson 4: Exterior Angles of Triangles Example #2: Suppose Angle 1 = 65° and

Lesson 4: Exterior Angles of Triangles Example #2: Suppose Angle 1 = 65° and Angle 4 = 125°, what is the measure of Angle 3? Angle 1 + Angle 3 = Angle 4 65 + Angle 3 = 125 -65 Angle 3 = 60° 4 2 1 3

Lesson 4: Exterior Angles of Triangles Example #3: 50° 3 x x+26

Lesson 4: Exterior Angles of Triangles Example #3: 50° 3 x x+26

Lesson 4: Exterior Angles of Triangles Example #3: Solve for x. Find each angle.

Lesson 4: Exterior Angles of Triangles Example #3: Solve for x. Find each angle. 50 + x + 26 = 3 x 76 + x = 3 x - x -x 76 = 2 x 38 = x 50° x+26 3 x 3(38) = 114 38 + 26 = 64 Angles 50 + 64 = 114

Lesson 4: Exterior Angles of Triangles Example #4: 4 x + 7 x+ 6

Lesson 4: Exterior Angles of Triangles Example #4: 4 x + 7 x+ 6 123°

Lesson 4: Exterior Angles of Triangles Example #4: Solve for x. Find the angles.

Lesson 4: Exterior Angles of Triangles Example #4: Solve for x. Find the angles. 4 x + 7 + x + 6 = 123 5 x + 13 = 123 -13 5 x = 110 x = 22 4 x + 7 4(22) + 7 = 95 22 + 6 = 28 95 + 28 = 123 x+ 6 123°

Practice • Guided, Independent, Extra Practice • The Exterior Angle Theorem • Handout 4

Practice • Guided, Independent, Extra Practice • The Exterior Angle Theorem • Handout 4

Closure Question: What is the Exterior and Remote Interior Sum Theorem? Exit Ticket Homework:

Closure Question: What is the Exterior and Remote Interior Sum Theorem? Exit Ticket Homework: Homework 4

Exit Ticket 1. Find the missing angle. x° 34° 65° 2. Find the missing

Exit Ticket 1. Find the missing angle. x° 34° 65° 2. Find the missing angle. x° 65° 125°

Homework 1. 65˚ 2. 65˚ 3. 24˚, 48˚, 108˚ 4. 45˚, 90˚ 5. 112˚

Homework 1. 65˚ 2. 65˚ 3. 24˚, 48˚, 108˚ 4. 45˚, 90˚ 5. 112˚ 6. 62˚ 7. 45˚ 8. <A = 47˚, <B = 90˚, <C = 43˚ 9. 105˚ 10. 120˚, 30˚ 11. 90˚, 60˚, 30˚ 12. 53˚, 55˚, 72˚ 15. C