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 2: The sum of two interior angles in a triangle, is equal to the exterior of the third F G HI Angle GHI = 7x + 9 Angle FGH = 60 Angle GFH = 4x + 12

6. Try the following in your notebooks: Angle BCD = 6x +12 Angle ABC = 70 Angle BAC = 4x + 18 A B CD X= ____ Angle BCD = _____ Angle BCA = ____