Question

the measures of two complementary angles have a ratio of 3 : 7. Set up and solve an equation to determine the measurements of the two angles

Answer 1

complementary angles add up to 90 degrees

3 : 7....added = 10

3/10 * (90) = 270/10 = 27
7/10 * (90) = 630/10 = 63

Answer 2

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:

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