Question

day 3 - wednesday, september 10th true or false: if two angles are supplements of the same angle, they must be congruent. explain briefly.

Explanation:

Let the angle be $\angle x$. Let $\angle A$ and $\angle B$ be its supplements. So $\angle A + \angle x=180^{\circ}$ and $\angle B+\angle x = 180^{\circ}$. By the subtraction property of equality, $\angle A=180^{\circ}-\angle x$ and $\angle B = 180^{\circ}-\angle x$. Thus, $\angle A=\angle B$, meaning they are congruent.

Answer:

True