Final answer:
To justify the statement that a triangle is equiangular if the sum of any two angles is equal to two times the measure of the third angle algebraically, assign variables to the angles and use algebraic manipulations to prove that all three angles are equal.
Step-by-step explanation:
To justify the statement algebraically, we can assign variables to the angles of the triangle. Let's say the angles are A, B, and C. According to the given condition, the sum of any two angles, let's say A and B, is equal to two times the measure of the third angle, C. This can be represented algebraically as A + B = 2C. To show that the triangle is equiangular, we need to prove that all three angles are equal. From the previous equation, we have C = (A + B)/2. If we substitute this back into the equation, we get A + B = 2((A + B)/2), which simplifies to A + B = A + B. This shows that the measure of all three angles is equal, thus the triangle is equiangular.
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