The power of the Triangle Sum Conjecture cannot be understated. Many of the upcoming problem solving activities and proofs of conjectures will require a very good understanding of how it can be used. Let us demonstrate a typical example:
Problem: Suppose that we are given triangle ABC such that:
Solution: We know that the sum of the angles must be 180 degrees. Since angles A and B already add up to 120 degrees, this leaves 60 degrees for angle C. Using algebra, this can be represented by:
A + B + C = 180
40 + 80 + C = 180
120 + C = 180
C = 60
So this conjecture tells us that if we know two of the angles in a triangle, then we can find the third angle quite simply.
Conjecture (Triangle Sum ): The sum of the interior angles in any triangle is 180 degrees.