Is it always true, sometimes true, or never true that two complementary angles have a common vertex?
I believe that it is always true. Complementary angels add up to 90 degrees.
Wait, sometimes true.
Sometimes. The angles can be anywhere in a figure as long as they add up to 90 degrees. Consider for example the acute angles of a right triangle
To determine whether it is always true, sometimes true, or never true that two complementary angles have a common vertex, we need to understand what complementary angles are.
Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.
Now, let's consider the scenario where angle A and angle B are complementary but do not have a common vertex. In this case, we would have two separate angles that add up to 90 degrees but are not connected at any point. However, this is not possible because for two angles to be complementary, they need to share a common side or vertex.
Therefore, it is always true that two complementary angles have a common vertex.