1. Interior and Exterior Angles of a Triangle

2. What do we know about triangles? All three interior angles add to 180. The exterior angle is supplement (adds to 180) with the interior angle. a b c d

3. Example 1: Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 A B C D Consider: 80 + (3x – 4) + Angle BCA = 180 Angle BCA + (5x + 8) = 180 *Both statements have 180 and Angle BCA

4. Example 1: Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 A B C D Which means: 80 + (3x – 4) = 5x + 8 We say that the sum of two interior angles is equal to the exterior of the third. 80 + (3x – 4) = 5x + 8 3x + 76 = 5x + 8 68 = 2x 34 = x

5. Example 1: Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 A B C D If x = 34: Angle BCD = 5x + 8 =5(34) + 8 =170 + 8 =178° Angle BAC = 3x – 4 = 3(34) – 4 = 102 – 4 = 98°

6. Example 2: F G H I Angle GHI = 7x + 9 Angle FGH = 60 Angle GFH = 4x + 12 Two interior angles: Angle FGH and Angle GFH Exterior angle: Angle GHI The sum of the interior angles is equal to the exterior: 4x + 12 + 60 = 7x + 9 4x + 72 = 7x + 9 63 = 3x x = 21