Interior and Exterior Angles of Triangles

Directions: In triangle ABC, angle ABC is obtuse. Using the digits 1 to 9 at most one time each, place a digit in each box to make angle ACB the smallest possible acute angle.

Hint

What does the first number in the three-digit number have to be?
What does the first number in the obtuse angle have to be?
What numbers do not work as the first digit of the acute angle? Why?

Answer

42 Degrees
138 = 96 + 42
137 = 95 + 42

Source: Jay Sydow

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