find the measure of an angle whose complement and supplement sum up to 126 degrees
Well, well, well, aren't we playing with angles today? To find the measure of an angle whose complement and supplement sum up to 126 degrees, we must embrace our mathematical wit.
Let's start by defining the angle as 'x.' The complement of angle 'x' is calculated by subtracting 'x' from 90 degrees, and the supplement can be found by subtracting 'x' from 180 degrees. So, we have two lovely equations:
Complement of 'x' + Supplement of 'x' = 126 degrees
(90 - x) + (180 - x) = 126
Now, if we simplify it a bit more, we get:
270 - 2x = 126
Ah, how intriguing! We can now solve the equation for 'x':
-2x = 126 - 270
-2x = -144
x = (-144)/(-2)
x = 72
Voila! The measure of the angle is 72 degrees. So, this little angle zips around, being all complementary and supplementary, and ends up measuring a delightful 72 degrees. Quite the amusing journey, if you ask me!
Let's denote the measure of the angle as x.
The complement of an angle is defined as 90 degrees minus the angle, so the complement of angle x is (90 - x) degrees.
The supplement of an angle is defined as 180 degrees minus the angle, so the supplement of angle x is (180 - x) degrees.
We are given that the sum of the complement and the supplement of angle x is 126 degrees. Therefore, we can set up the equation:
(90 - x) + (180 - x) = 126
Simplifying the equation:
90 - x + 180 - x = 126
270 - 2x = 126
Rearranging the equation:
-2x = 126 - 270
-2x = -144
Dividing both sides by -2:
x = -144 / -2
x = 72
Therefore, the measure of the angle is 72 degrees.
To find the measure of an angle whose complement and supplement add up to 126 degrees, we can use the definitions of complement and supplement.
The complement of an angle is the angle that, when added to the original angle, equals 90 degrees. Similarly, the supplement of an angle is the angle that, when added to the original angle, equals 180 degrees.
Let's represent the original angle as 'x'. The complement of 'x' would be (90 - x) degrees, and the supplement of 'x' would be (180 - x) degrees.
According to the problem, the complement and supplement of the angle sum up to 126 degrees. Therefore, we can write the following equation:
(90 - x) + (180 - x) = 126
Simplifying the equation:
270 - 2x = 126
Next, we can solve for 'x' by isolating it on one side of the equation:
-2x = 126 - 270
-2x = -144
Finally, divide both sides of the equation by -2 to solve for 'x':
x = -144 / -2
x = 72
Therefore, the measure of the angle is 72 degrees.
complement of angle X=90-X
supplement of angle X=180-X
=>
complement (C) =supplement (S) -90
C+S=126
C+(C+90)=126
2C=126-90
Solve for C and hence X.