Question

One of two complementary angles is 8 degrees less than the other.
Which of the following systems of equations represents the word problem?

x + y = 90 and x - y = 8
x + y = 90 and 90 - x = 8
x + y = 90 and y = 8x

Answer 1

I think it is the middle one becuase complimentary angles add up to 90 degrees and if one is 8 less than the other it would be proved like that.

Answer 2

Answer:  The correct option is

$(A)~~x+y=90,~~x-y=8.$

Step-by-step explanation:  Given that one of the two complementary angles is 8 degrees less than the other.

We are to select the correct system of equations represents the given word problem.

Let x and y represents the two complementary angles where y is less than x.

Since one angle is 8 degrees less than the other and y is less than x, so we have

$x-y=8.$

We know that the sum of two complementary angles is 90 degrees, so we get

$x+y=90.$

Thus, the required system of equations representing the given word problem will be

$x+y=90,\\\\x-y=8.$

Option (A) is CORRECT.