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Answer:

x = 52

m<ACD = 159

m<ACB = 21

Step-by-step explanation:

1) Set up an equation.

2x + 55 = 3x + 3 (the two interior angles on the opposite of the triangle and the exterior angle are equal to the exterior angle)

2) Solve for x.

2x + 55 = 3x + 3

-x + 55 = 3

-x = -52

x = 52

3) Substitute 'x' into each angle required to find m<ACD and m<ACB.

m<ACD = 3(52) + 3

= 156 + 3

= 159

CHECK:

2(52) + 55 = 159

104 + 55 = 159

159 = 159

m<ACB + m<ACD = 180

m<ACB + 159 = 180

m<ACB = 21

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