the complement of an angle is 18 degree more than the angle.find the measure of the angle and its complement.
let the angle be x
then its complement is 90-x
90-x = x + 18
-2x = -72
x = 36
check:
the angle is 36° and its complement is 54°
which is 18° more than 36°
Well, well, well! We have ourselves a math problem, don't we? Let's dive right into it!
Let's call the angle we're looking for "x". According to our problem, the complement of x, which we can call "y", is 18 degrees more than x.
So, if we were to write this in an equation, it would be y = x + 18.
Now, we know that the sum of an angle and its complement is equal to 90 degrees. In other words, x + y = 90.
Since we already have an equation for y, we can substitute it into the second equation. So, x + x + 18 = 90.
Simplifying this equation will give us 2x + 18 = 90.
To solve for x, we subtract 18 from both sides: 2x = 90 - 18.
Therefore, 2x = 72.
And when we divide both sides by 2, we find that x = 36.
So, the measure of the angle is 36 degrees. To find the complement, we substitute x back into the first equation: y = 36 + 18.
After doing the math, we find that y = 54.
Hence, the measure of the angle is 36 degrees, and its complement is 54 degrees.
Now, wasn't that an angle-larious problem to solve?
Let's denote the angle we're looking for as x.
The complement of this angle is 18 degrees more than the angle, so the measure of the complement can be expressed as x + 18.
Since the sum of an angle and its complement is always 90 degrees (by definition of complementary angles), we can set up the equation:
x + (x + 18) = 90
Combining like terms, we get:
2x + 18 = 90
Next, we subtract 18 from both sides:
2x = 72
Finally, we divide both sides by 2:
x = 36
So, the angle measures 36 degrees and its complement measures 36 + 18 = 54 degrees.
To solve this problem, we can start by defining the given information:
Let's say the measure of the angle is x degrees.
According to the given statement, the complement of this angle (90 degrees minus the angle) is 18 degrees more than the angle. So, we can express this mathematically as:
90 - x = x + 18
Now, we can solve this equation to find the value of x, which represents the measure of the angle:
90 - x = x + 18
90 - 18 = x + x
72 = 2x
x = 72/2
x = 36
Therefore, the measure of the angle is 36 degrees.
To find the complement of the angle, we subtract the angle from 90 degrees:
90 - 36 = 54
Hence, the measure of the complement angle is 54 degrees.