Question

The ratio of the measures of two complementary angles is 7:8 what is the measure of the largest angle

Answer 1

complimentary angles add up to 90

7:8.....added = 15......this means that 7/15 of 90 is one angle and 8/15 of 90 is the other angle.

7/15 * 90 = 42
8/15 * 90 = 48 <== largest angle

Answer 2

First represent the angles as 7x and 8x.

Let's call 7x an angle and 8x its complement.

Now, remember that if two angles are complementary,

then the sum of their measures is 90 degrees.

So we can setup the equation 7x + 8x = 90.

Now combine like terms on the left side to get 15x = 90.

Now, dividing both sides by 15, we find that x = 6.

So the measure of our first angle, 7x, is 7(6) or 42° and

the measure of its complement, 8x, is 8(6) or 48°.

Finally, notice that if we add our two angles together,

we have 42 + 48 which is 90 so our answer checks.