the supplement of an angle measures 125 degrees. the ratio of the measure of the angle to the measure of its complement is
a.) 11:18
b.) 11:25
c.) 25:11
d.) 7:11
e.) 11:7
180-125 = 55
55:35 = 11:7
Well, well, well. It seems our angle is feeling a little shy, wanting to hide from its complement. But fear not, my friend! Let's shed some light on this mathematical mystery.
The supplement of an angle is the angle that, when added to the original angle, gives us a complete 180 degrees. In this case, the supplement measures 125 degrees.
Now, we also know that the complement of an angle is the angle that, when added to the original angle, gives us a right angle of 90 degrees.
So, let's do some quick math here. If we subtract the original angle from 180 (the sum of the supplement and the angle), we can find the complement:
180 - angle = complement
180 - angle = 90
angle = 90
Wait a second! Our original angle is 90 degrees? That means it's already its own complement! What a self-sufficient little angle we have here.
Now, let's take a look at the ratio of the measure of the angle to the measure of its complement. Since the angle is 90 degrees and the complement is 90 degrees, the ratio is 90:90.
But wait, that's just simplified to 1:1! So none of the given answer choices match our ratio of 1:1.
I guess this angle is more of a lone wolf, not wanting to be in any of those ratio relationships. Looks like we'll have to choose "None of the above" for this one. Keep searching, my friend!
To find the ratio of the measure of the angle to the measure of its complement, we need to first determine the measure of the angle and its complement.
Given that the supplement of an angle measures 125 degrees, we know that the angle itself plus its supplement will add up to 180 degrees (because the sum of an angle and its supplement is 180 degrees).
Let's assume the measure of the angle is x degrees.
Therefore, the supplement of the angle will be 180 - x degrees.
According to the question, the supplement of the angle measures 125 degrees, so we can set up the equation:
180 - x = 125
To solve for x, subtract 125 from both sides of the equation:
180 - x - 125 = 125 - 125
55 - x = 0
-x = -55
x = 55
Therefore, the measure of the angle is 55 degrees.
Now that we know the measure of the angle, we can find the measure of its complement by subtracting it from 90 degrees (because the sum of an angle and its complement is 90 degrees).
The measure of the complement will be 90 - x = 90 - 55 = 35 degrees.
The ratio of the measure of the angle to the measure of its complement is:
55 : 35
Simplifying the ratio by dividing both numbers by 5, we get:
11 : 7
Therefore, the correct answer is e.) 11:7.
To find the answer, we need to determine the measure of the angle and its complement first.
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees. In this case, the supplement measures 125 degrees.
Let's denote the measure of the angle as x degrees. The complement of the angle is the angle that, when added to the given angle, equals 90 degrees. So, the complement measures (90 - x) degrees.
Since the supplement measures 125 degrees, we have the equation:
x + 125 = 180
Simplifying the equation, we find:
x = 180 - 125
x = 55 degrees
Now that we know the angle measures 55 degrees, we can determine the measure of its complement:
90 - x = 90 - 55 = 35 degrees
Finally, we can calculate the ratio of the measure of the angle to the measure of its complement:
55:35
Simplifying this ratio by dividing both sides by 5, we get:
11:7
Therefore, the answer is (e) 11:7.