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.

"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.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

answer: hey there,

the answer you are looking for is a..

hope this you!