Question

If the ratio of two complementary angles is 4 to 5, explain how you would set up an equation to solve for the angle measures.

Answer 1

To find two complementary angles with a ratio of 4 to 5, set up the equation 4x + 5x = 90, where x is the common multiplier. Solve for x to find each angle's measure. Check that the sum equals 90 degrees to confirm the solution.

Step-by-step explanation:

To determine the measures of two complementary angles with a ratio of 4 to 5, you first need to understand that complementary angles add up to 90 degrees. Let's call the angles A and B, with A being the smaller angle. Since they are in a ratio of 4 to 5, we can represent them as 4x and 5x, respectively, where x is a common multiplier. The equation to solve for x is set up based on the definition of complementary angles:

4x + 5x = 90

Combine like terms to simplify:

9x = 90

Now, divide both sides by 9 to solve for x:

x = 90 ÷ 9

x = 10

Once you have the value of x, you can find the measures of the angles:

A = 4x = 4(10) = 40 degrees

B = 5x = 5(10) = 50 degrees

Always check your answer to confirm it makes sense. In this case, A + B should equal 90 degrees, which it does (40 + 50 = 90).

Answer 2

"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5

For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say

x/y = 4/5

also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.

Let's cross multiply on the first equation to get...

x/y = 4/5

5*x = 4*y

Now replace y with 90-x. Solve for x

5x = 4(90-x)

5x = 360 - 4x

5x+4x = 360

9x = 360

x = 360/9

x = 40

Use this to find y

y = 90 - x = 90 - 40 = 50

So the two angles are 40 degrees and 50 degrees.