|
Question 626388: The complement of an angle, A, in degrees, is equal to one-fifth of the supplement of the angle, also in degrees. Then A =
A) 15°
B) 20°
C) 30°
D) 40°
E) 45°
F) 50°
G) 60°
H) 72°
I) 80°
J) none of these
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! As you know, writing expressions is a key skill in solving word problems. A common situation that arises is when you have two numbers you don't know but you know what they add up to. For example, let's say we have two numbers which add up to 120. A way to use just one variable to express both of these numbers is this:
Let x = one of the numbers. The other number can then be expressed as 120 - x. Knowing this will be very helpful with your problem.
Complements are two angles that add up to 90 and supplements are two angles that add up to 180. So is one angle is called A, then we can call its complement 90 - A and it supplement 180 - A. Now we just do some basic translation:
The complement of an angle A is equal to one-fifth of the supplement of the angle
90 - A = 1/5 * (180 - A)
We know have an equation we can solve. Multiplying out the right side we get:
90 - A = 36 - (1/5)A
We can eliminate the fraction by multiplying both sides by 5:
450 - 5A = 180 - A
Adding 5A to each side:
450 = 180 + 4A
Subtracting 180 from each side:
270 = 4A
Divide both sides by 4:
270/4 = A
which reduces to
A = 67.5 degrees
Check: The complement of of 67.5 would be 90 - 67.5 or 22.5 degrees. The supplement of 70 would be 180 - 67.5 = 112.5 degrees. and 22.5 is equal to (1/5)*112.5 so this answer is correct, making "None of these" the correct answer to your problem.
|
|
|
| |
