The measures of two complementary angles are in the ratio 1 : 5. Find the angles.
Complementary angles are one of the most important concepts of angles. Two angles are called complementary if their measures add to 90 degrees. For example, 40 and 50 degrees are complementary to each other.
Answer: The measures of two complementary angles which are in the ratio 1: 5 are 15 degrees and 75 degrees.
Let us understand how we arrived at the solution.
Let the angles be x and 5x, according to the given ratio.
According to the rule of complementary angles:
⇒ x + 5x = 90
⇒ 6x = 90
⇒ x = 15, hence, 5x = 75