Find the measure of two complementary angles if the measure of one angle is 5/8 the measure of the other. What is the measure of the larger angle? What is the measure of the smaller angle?
(3/8) * 90 = 270/8 = ?
idk the formula, but simply taking ⅝ of 90° is not correct.
I would convert the fractions to decimals, giving you 0.625 and 0.375 (you can drop the zeros in your calculations, just don't forget the decimal!).
Then, ***MAYBE***: 0.375:n = 0.625:(n * 0.375), where n is the larger angle (I never have been good with ratios!)
Or, maybe: (.375 • n) + n = 90
Trial and error yields this:
55.375/34.625 = .625282
55.38 34.62 = .6251354
34.618/55.382 = .6250767, and
34.615/55.385 = .6249887;
but, there's got to be a better way!
Ms. Sue may very well be on the right track, but it seems that's just taking ⅝ and 3/8 of 90. The results of those calcs are 33.75 and 56.25, and the smaller is not ⅝ the larger (56.25 * .625 = 35.15625, not 33.75).
Clear as mud? Look up ratios and see if you can't apply them here.
Or, as Richard Bach wrote in "Illusions, the Adventures of a Reluctant Messiah,"
>Everything in this book may be wrong.<
Hope this helps!
one angle is 5x and the other is 8x
So, 5x+8x = 90
x = 90/13
Now you can figure the two angles.
To find the measure of the larger and smaller angles, let's assign variables to the angles. Let x represent the measure of the larger angle and y represent the measure of the smaller angle.
From the given information, we know that one angle is 5/8 the measure of the other. Therefore, we can set up the following equation:
x = (5/8)y
We also know that complementary angles add up to 90 degrees. So we can write:
x + y = 90
Now we have a system of two equations:
x = (5/8)y
x + y = 90
To solve the system of equations, we can substitute the value of x from the first equation into the second equation:
(5/8)y + y = 90
Add the y terms:
(13/8)y = 90
To isolate y, we multiply both sides by the reciprocal of (13/8), which is (8/13):
y = (90)(8/13)
y = 720/13
Therefore, the measure of the smaller angle is 720/13 degrees.
To find the measure of the larger angle, plug the value of y into the first equation:
x = (5/8)(720/13)
Multiply the fractions:
x = (5*720)/(8*13)
x = 3600/104
Simplify the fraction:
x = 225/26
Therefore, the measure of the larger angle is 225/26 degrees.