The supplement of an angle X is four times as large as the complement of the angle. Write an equation to find X.
Responses
A 60°60°
B 27°27°
C 30°30°
D 45°45°
E 36°
Let's start by defining the supplement and complement of an angle:
- The supplement of an angle is the angle that, when added to the original angle, forms a straight line (180 degrees). So, if the original angle is X, then its supplement is 180 - X.
- The complement of an angle is the angle that, when added to the original angle, forms a right angle (90 degrees). So, if the original angle is X, then its complement is 90 - X.
Now, we are told that the supplement of angle X is four times as large as its complement. Using the definitions above, we can write this as an equation:
180 - X = 4(90 - X)
Simplifying and solving for X:
180 - X = 360 - 4X
3X = 180
X = 60
Therefore, the answer is A) 60 degrees.