Unit 8 Angle Relationships Lesson 3 Interior Angles

Unit 8 Angle Relationships Lesson 3 Interior Angles of Triangles

Lesson 3: Interior Angles of Triangles Objective: SWBAT find the measures of interior angles in a triangle. Do Now:

Lesson 3: Interior Angles of Triangles A triangle is formed by 3 line segments that intersect only at their end points. The angle formed by the segments that lies inside the triangle is an interior angle. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°.

Lesson 3: Interior Angles of Triangles Ex #1: Find the measure of the missing angle. 125° 15 25° x°

Lesson 3: Interior Angles of Triangles Ex #1: Find the measure of the missing angle. 125 + x = 180 150 + x = 180 -150 X = 30 Angle is 30° 125° x° 15 25°

Lesson 3: Interior Angles of Triangles Ex #2: Find the measure of the missing angle. 30° x°

Lesson 3: Interior Angles of Triangles Ex #2: Find the measure of the missing angle. 30° 90 + 30 + x = 180 120 + x = 180 -120 x = 60 Angle is 60° x°

Lesson 3: Interior Angles of Triangles Ex #3: Find the measure of each angle. x 50°

Lesson 3: Interior Angles of Triangles Ex #3: Find the measure of each angle. x 50° This is an isosceles triangle, therefore if the two sides are equal then the two angles are equal. 50 + x = 180 100 + x = 180 -100 x = 80 Angles are 50°, 50° and 80°

Lesson 3: Interior Angles of Triangles Ex #4: Find the measure of each angle. 15 15 15

Lesson 3: Interior Angles of Triangles Ex #4: Find the measure of each angle. 15 15 15 Since all sides are equal, this is an equilateral triangle. Therefore all angles must be equal. 180/3 = 60 Each angle is 60°

Lesson 3: Interior Angles of Triangles Ex #5: Find the measure of the missing angle. 2 x° x°

Lesson 3: Interior Angles of Triangles Ex #5: Find the measure of the missing angle. 2 x° 2 x + 90 = 180 3 x + 90 = 180 -90 = -90 3 x = 90 x = 30 x° 2(30)=60 Angles are 30°, 60° and 90°

Lesson 3: Interior Angles of Triangles Ex #6: Find the measure of each angle. 9 x-2 3 x 4 x-10

Lesson 3: Interior Angles of Triangles Ex #6: Find the measure of each angle. 9 x-2 3 x 3 x + 9 x – 2 + 4 x – 10 = 180 16 x -12 = 180 +12 = +12 16 x = 192 x = 12 3(12) = 36 9(12)-2 = 106 4(12)-10 = 38 Angles are 36°, 106° and 38° 4 x-10

Lesson 3: Interior Angles of Triangles Ex #7: The measures of the angles of a triangle are in the ratio 5: 6: 9. What is the measure of each angle?

Lesson 3: Interior Angles of Triangles Ex #7: The measures of the angles of a triangle are in the ratio 5: 6: 9. What is the measure of each angle? 5 x + 6 x + 9 x = 180 20 x = 180 x=9 5(9) = 45 6(9) = 54 9(9) = 81 Angles are 45°, 54° and 81°

Challenge Ex #8: Suppose Angle 1 = 65° and Angle 2 = 55°, what is the measure of Angle 4? 2 1 3 4

Practice • Practice, Skills and Problem Solving • Handout 3

Closure Question: What is the Triangle Sum Theorem? Exit Ticket Homework: Homework 3

Exit Ticket 1. Find the missing angle. 65° 34° x° 2. Find the missing angles. 10 x + 20° 3 x°