If two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.
Two angles are said to be complementary if their sum is equal to 90º.
Answer: 15º and 75º are the two complementary angles that have their measures in the ratio of 1 to 5.
Let's solve this question step by step.
Given: The ratio of two complementary angles is 1:5
Let the common factor of the given two angles be x. Then, the angles are x and 5x.
Applying the condition for complementary angles, we get:
x + 5x = 90º
⇒ 6x = 90º
⇒ x = 90º/6
⇒ x = 15º
The other given angle is 5x.
Thus, 5x = 5 × 15º = 75º [Since, x = 15º]
Hence, the two required angles are 15º and 75º
We can calculate complementary angles by using a complementary angles calculator.