The measurements of the two complementary angles whose ratio is 3:7 is obtained as 27° and 63°
What are complementary angles?
Two angles whose sum is 90° are called complementary angles.
Let we assume that:
- The first angle be of x°
- The second angle be of y°
Then as the angles are complementary, so we get:
\(x+y = 90\)
Also, we're given that:
\(x:y = 3:7\), or, in fraction, we get: \(\dfrac{x}{y} = \dfrac{3}{7}\)
From second equation, we get x in terms of y as:
\(\dfrac{x}{y} = \dfrac{3}{7}\\\\\text{Multiplying y on both the sides}\\\\x = \dfrac{3y}{7}\)
Substituting this value of x in first equation, we get:
\(x + y = \dfrac{3y}{7} + y =90\\\\\dfrac{3y}{7} + \dfrac{7y}{7} = 90\\\\\dfrac{10y}{7} = 90\\\\\text{Multiplying 7 on both the sides}\\\\10y = 630\\\\y = 63\)
Substituting this value of y in expression for x:
\(x = \dfrac{3y}{7} = \dfrac{3 \times 63}{7} = 27\)
Thus, the measurements of the two complementary angles whose ratio is 3:7 is obtained as 27° and 63°
Learn more about complementary angles here:
https://brainly.com/question/2882938
