The measure of an angle is 4 times the measure of its complement. What is the measure of the angle's supplement?
18
18 is the complementary angle. Now find the supplementary angle.
18 + X = 180
http://www.mathsisfun.com/geometry/supplementary-angles.html
The measure of an angle is 4 times the measure of its complement. What is the measure of the angle's supplement?
To solve this problem, let's start by understanding the terms related to angles. The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
Let's assume the measure of the angle is x degrees. According to the problem, the measure of the angle is 4 times the measure of its complement. Mathematically, we can represent this as:
x = 4 * (90 - x)
Now, let's solve the equation to find the value of x:
x = 4 * 90 - 4 * x
x = 360 - 4x
5x = 360
x = 72
Therefore, the measure of the given angle is 72 degrees.
Now, to find the measure of the angle's supplement, we subtract the measure of the angle from 180 degrees:
Supplement = 180 - 72
Supplement = 108
So, the measure of the angle's supplement is 108 degrees.
5x = 90
x = ?
let the angle be x
then its complement is 90-x
x = 4(90-x)
x = 360 - 4x
5x = 360
x = 72
so the angle is 72°
and its supplement is 180-72 = 108°
check:
our angle = 72
its complement = 18
is the angle 4 times its complement ?
is 72 = 4(18) ? yes