SOLUTION: Dealing with contradictions: Is is possible to draw a triangle in which the sum of any two angles is less than 120 degrees.

Question 32756: Dealing with contradictions: Is is possible to draw a triangle in which the sum of any two angles is less than 120 degrees.
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
The answer is no.
Assume that it is possible to draw a triangle in which the sum of any two angles is less than 120 degrees.... (1)
Consider A, B, and C as three angles of the triangle.
Based on (1):
A+B < 120
B+C < 120
A+C < 120
Summing all three produces 2A+2B+2C < 360
=> 2(A+B+C) < 360
=> (A+B+C) < 180
But, sum of all three angles of a triangle is 180.
Thus, it is not possible to draw a triangle in which the sum of any two angles is less than 120 degrees.
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