Two angles are complementary to each other, if the ratio of the two angles is 3:2, then what is the difference of measures in degree of these two angles?
please explain :(
complementary angles add up to 90°
let the two angles be 3x and 2x,
then their difference is x
but 3x + 2x = 90
5x = 90
x = 18
the difference in the two angles is 18°
check:
one is 3(18) = 54
the other is 2(18) = 36
and what is their difference ??
To find the difference in the measures of two complementary angles, we first need to determine the measures of the individual angles.
Let's assume that the two angles are x and y, where x and y are the measures of the angles in degrees.
According to the given information, the ratio of the two angles is 3:2. This means that
x/y = 3/2
To find the values of x and y, we need another equation. Since the two angles are complementary, we know that their sum is equal to 90 degrees. Therefore, we can write:
x + y = 90
Now we have a system of two equations:
x/y = 3/2
x + y = 90
We can solve this system of equations to find the values of x and y.
Multiplying the first equation by 2, we get:
2(x/y) = 3
Expanding, we have:
2x/y = 3
Cross-multiplying, we find:
2x = 3y
Rearranging, we get:
x = (3y)/2
Now substitute x in the second equation with the value we found:
(3y)/2 + y = 90
Adding the terms with y gives us:
(3y + 2y)/2 = 90
Combining like terms, we have:
(5y)/2 = 90
To eliminate the fraction, we can multiply both sides of the equation by 2:
5y = 90 * 2
5y = 180
Now we can solve for y by dividing both sides by 5:
y = 180 / 5
y = 36
Substituting this value back into the first equation to find x:
x = (3y)/2 = (3*36)/2 = 54
Therefore, the measures of the two angles are x = 54 degrees and y = 36 degrees.
To find the difference in the measures of these angles, subtract the smaller angle from the larger angle:
Difference in measures = x - y = 54 - 36 = 18 degrees.
So, the difference in the measures of these two angles is 18 degrees.