Five times the measure of an angle is 48 more than the measure of its supplement. Find the measure of the angle.
let the measure of the angle be x
5x = (180 - x) + 45
5x = 180 - x + 45
6x = 225
x = 37.5°
check:
5 times the angle = 187.5
the supplement of 37.5 is 142.5
is 187.5 45 more than 142.5 ?
To find the measure of the angle, let's start by defining the angle. Let's call the angle x.
According to the problem, five times the measure of the angle is 48 more than the measure of its supplement. The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
So, we can write this information as an equation:
5x = (180 - x) + 48
Now, let's solve the equation to find the value of x.
First, simplify the right side of the equation:
5x = 180 - x + 48
Combine like terms:
5x + x = 180 + 48
Simplify further:
6x = 228
Next, isolate x by dividing both sides of the equation by 6:
x = 228 / 6
Now, solve for x:
x = 38
Therefore, the measure of the angle is 38 degrees.