The measure of two complementary angles are in the ratio 7:11. What is the measure of the smaller angle?
Would the correct answer be 35?
7x+11x=90
18x=90
x=5
7x=35
11x=55
you got it.
35
Well, that's a pretty "angle-ic" question! If the measure of two complementary angles are in the ratio 7:11, we can find the value of the smaller angle by dividing the total ratio (7 + 11 = 18) by the sum of the ratios (7 + 11). So, the smaller angle would be (7/18) * 90 degrees, which is approximately 35.56 degrees. But hey, rounding it down to 35 wouldn't make you a "corner-cutting" mathematician!
Yes, the correct answer is 35. To determine the measure of the smaller angle, we need to find the values of both angles.
Let's assume the smaller angle measures x degrees. Since the angles are complementary, the larger angle can be expressed as (90 - x) degrees.
According to the given ratio, the measure of the larger angle (90 - x) is 11 times the measure of the smaller angle (x). So we can write the proportion:
(90 - x) / x = 11 / 7
To solve this proportion, we can cross-multiply:
7 * (90 - x) = 11 * x
630 - 7x = 11x
Combine like terms:
630 = 18x
Now, divide both sides by 18:
x = 630 / 18
Simplify:
x = 35
So the measure of the smaller angle is 35 degrees.