My teacher gave me a question like this......
Complements of the same angle are __________ complementary
Sometimes/ Never/ Always
The correct answer is Sometimes, BUT WHY?
if both angles are x, then both complements are 90-x, right?
So, they are equal.
But, if they are both 45°, then they are also complementary.
So, sometimes
That's exactly what I was thinking, thx!
To understand why the answer is sometimes, we need to understand what complements of an angle are.
Complements of an angle are two angles that add up to 90 degrees. In other words, if you have an angle x and its complement y, then the sum of x and y will be 90 degrees.
Now, let's consider the given statement: "Complements of the same angle are __________ complementary." Here, we are talking about the complements of the same angle, which means we have one angle and we are finding the complement of that angle.
In general, when we have one angle and we find its complement, the sum will always be 90 degrees. Therefore, the statement "Complements of the same angle are always complementary" is correct because it always holds true.
However, there can be special cases where the statement might not hold true, leading to the answer "Sometimes." For example, consider an angle of 45 degrees. Its complement would be 45 degrees as well, and the sum of these angles would be 90 degrees, making them complementary. However, if we take an angle of 0 degrees, its complement would be 90 degrees, and the sum of these angles would also be 90 degrees, making them complementary again.
Thus, in some cases, the complements of the same angle can be complementary, while in other cases, they may not be. Therefore, the correct answer is sometimes.