SOLUTION: find the number of degrees in an angle that measures 8 degrees less than its complement.

Question 116488: find the number of degrees in an angle that measures 8 degrees less than its complement.
Answer by jgr45(31) (Show Source): You can put this solution on YOUR website!
Find the number of degrees in an angle that measures 8 degrees less than its
complement.
__________________
Complementary angles always total 90 degrees. So we need to write an equation translating what we're given:
Number of degrees = a
Complement = b
The angle and its complement have a difference of 8, and they sum to 90. So we know that:
a+b=90 and a-b=8...so this becomes a system of equations to solve. This is a very convenient problem to solve by elimination:
2a=98
a=49
angle a=49 degrees; angle b=41 degrees.
There is also an alternate method, and it is so ridiculously easy that it doesn't even belong in an algebra book; it belongs in a math book because it doesn't even involve variables at all!
Whenever you are given the sum of two numbers and the difference of the same two numbers (as in this problem) and you are asked to find the numbers, here's what you do:
Take half of the sum and half of the difference, and the sum of those two and difference of those two, voila, are your solutions.
In our example, the sum of the numbers we're looking for is 90 and the difference between them is 8. So we halve both of these numbers (45 and 4) and then add and subtract them.
45 + 4 = 49, larger angle
45 - 4 = 41, smaller angle.
Another example: find two numbers whose sum is 428 and differ by 32.
Half of 428 is 214; half of 32 is 16.
214 + 16 = 230 (larger number)
214 - 16 = 198 (smaller number).
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