The measure of an angle's complement is 24 less than twice the measure of the angle. Find the measure of the angle and its complement.
a. 38, 52
b. 54, 36
c. 68, 112
d. 112, 68
(90-x)=2x-24
Looks like (a) to me
Well, let's figure this out using a little mathematical clown logic.
Let's call the measure of the angle x. According to the problem, its complement would then be 90 - x.
The problem also tells us that the measure of the complement is 24 less than twice the measure of the angle. So, we can write the equation:
90 - x = 2x - 24
Now, let's solve this equation to find the value of x:
90 + 24 = 2x + x
114 = 3x
x = 38
So, the measure of the angle is 38 degrees.
Now, to find the complement, we can substitute the value of x into the expression for the complement:
90 - 38 = 52
So, the complement of the angle is 52 degrees.
Therefore, the answer is option a: 38, 52.
To solve this problem, let's first assign a variable to represent the measure of the angle.
Let x be the measure of the angle.
According to the given information, the measure of the angle's complement is 24 less than twice the measure of the angle, which can be expressed mathematically as:
Complement of the angle = 2x - 24
Since we know that the sum of an angle and its complement is 90 degrees (because they form a right angle), we can set up the equation:
x + (2x - 24) = 90
Simplifying the equation:
x + 2x - 24 = 90
3x - 24 = 90
3x = 114
x = 38
So the measure of the angle is 38 degrees.
Now, to find the measure of the complement, substitute the value of x back into the equation for the complement of the angle:
Complement of the angle = 2x - 24
Complement of the angle = 2(38) - 24
Complement of the angle = 76 - 24
Complement of the angle = 52
Therefore, the measure of the angle is 38 degrees, and its complement is 52 degrees.
So the answer is option a. 38, 52.
angle A = X degree,
angle B = 2x-24 degrees,
A + B = 90o,
x + (2x-24) = 90,
X = 38o,
2x-24 = 2*38 - 24 = 52o.