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Interior and Exterior Angles of a Triangle

Interior and Exterior Angles of a Triangle. 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. b. a. d. c. Example 1:. Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4. B. Consider:

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Interior and Exterior Angles of a Triangle

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  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. b a d c

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

  4. Example 1: 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 Angle BCD = 5x +8 Angle ABC = 80 Angle BAC = 3x – 4 B A D C

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

  6. G Example 2: Angle GHI = 7x + 9 Angle FGH = 60 Angle GFH = 4x + 12 I H F 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

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