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.

a

b

c d

Example 1:

Angle BCD = 5x +8

Angle ABC = 80

Angle BAC = 3x – 4

A

B

C DConsider:

80 + (3x – 4) + Angle BCA = 180Angle BCA + (5x + 8) = 180*Both statements have 180 and Angle BCA

Example 1:Angle BCD = 5x +8

Angle ABC = 80

Angle BAC = 3x – 4

A

B

C D

Which means:80 + (3x – 4) = 5x + 8We say that the sumof two interior anglesis equal to the exteriorof the third.80 + (3x – 4) = 5x + 83x + 76 = 5x + 8

68 = 2x34 = x

Example 2:

• The sum of two interior angles in a triangle, is equal to the exterior of the third

F

G

H I

Angle GHI = 7x + 9Angle FGH = 60Angle GFH = 4x + 12

Try the following in your notebooks:

Angle BCD = 6x +12

Angle ABC = 70

Angle BAC = 4x + 18

A

B

C D

X= ____Angle BCD = _____Angle BCA = ____