two angles have a sum of 90 degrees. if their measures are in a ratio of 2:7, find the measure of the smaller angle

Answer 1

Aha! You can do this algebraically if you let the measure of the smaller angle be 2x and that of the larger angle be 7x.

For example, if the question said, "two angles have a sum of 115 degress. Their measures are in the ratio of 2:3. Find the measure of the larger angle," you could solve it this way:

Let the measure of the smaller angle be 2x. Then the measure of the larger angle must be 3x, so that their ratio is 2:3. Since the sum of their measures is 115 degrees, 2x + 3x = 115.

So 5x = 115.

Thus x = 23.

Finally, since we need to find the measure of the larger angle, and we know that it's 3x and that x is 23,

the answer is 3(23) = 69 degrees.

That's it; but if we want to do so, we can also check our solution, as follows:

Also the smaller angle measures 2x = 2(23) = 46. Thus the sum of the angles' measures is: 46 + 69,

which equals 115.

Chimpon!

Answer 2

2+7 = 9, so the entire proportion is out of 9

Ratio of 2 to 7 means the smaller angle is (2/9) * 90 = 20

and the larger angle is (7/9)*90 = 70

Another way to figure it is let x be the equal proportion amount.

2x + 7x = 90

9x = 90

x=10

so 2*10 = 20 and 7*10 = 70