Is it possible for supplementary angles to also be equal angles? Be sure to use proper mathematical terminology. Include numbers, pictures and/or words in your explanation.

Answer 1

No, supplementary angles cannot be equal angles.

Supplementary angles are two angles whose measures sum up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180.

Equal angles, on the other hand, are two angles that have the same measure. In symbols, if angle A and angle B are equal, then A = B.

Now, let's suppose that there are two supplementary angles, but they are also equal. This means that A + B = 180 and A = B.

If we substitute A = B into the first equation, we get B + B = 180, which simplifies to 2B = 180.

Dividing both sides of the equation by 2, we obtain B = 90.

However, this implies that A = B = 90, which contradicts the assumption that A and B are supplementary angles. This is because if A = 90 and B = 90, their sum would be 180, not less than 180.

Therefore, it is not possible for supplementary angles to also be equal angles.