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 36°36°
B 45°45°
C 60°60°
D 27°27°
E 30°
Let's first define the terms complement and supplement.
Complement: Two angles are complementary if their sum is 90 degrees.
Supplement: Two angles are supplementary if their sum is 180 degrees.
Now, let X be the angle in question. We know that its supplement is four times as large as its complement.
Supplement of X = 180 - X (because the sum of an angle and its supplement is 180)
Complement of X = 90 - X (because the sum of an angle and its complement is 90)
According to the problem statement,
180 - X = 4(90 - X)
Simplifying this equation:
180 - X = 360 - 4X
3X = 180
X = 60
Therefore, the answer is (C) 60 degrees.