Question 509927: Given any three positive real numbers, a, b, and c, with b less than 180 and c less than 180, can you construct a triangle having two interior angles whose measures are b and c, respectively, and the included side having measure a? Illustrate
Answer by Edwin McCravy(20055)   (Show Source):
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Not necessarily, because if b = c = 179°, then both requirements
b < 180° and c < 180° are met. However, b and c cannot be measures
of 2 interior angles of a triangle because just those two angles
alone have sum of measures 358°, and the sum of the measures of all
three interior angles of a triangle must have sum of only 180°. Two
of them can't have sum of measures 358° and yet all three have sum of
only 180°.
Edwin
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