Think about the locations of the angles in comparison to each other.
Sometimes
Practice makes perfect
We are asked to examine the following statement to determine if it is always, sometimes, or never true.
If two angles are complementary,
then they form a right angle.
The truth value of this statement depends on the position of the angles.
Adjacent Complementary Angles
The sum of the measure of complementary angles is 90. If the angles are adjacent, then together they form an angle of measure 90 — a right angle. So, it is possible that two complementary angles form a right angle.
Nonadjacent Complementary Angles
If the angles are not adjacent, then they do not form an angle at all. So, it is possible that two complementary angles do not form a right angle.
Conclusion
Sometimes two complementary angles form a right angle, but sometimes they do not.
