The measure of one angle is 30 degrees less than one-third the measure of its supplement. Find the two angles.
Let's assume that one angle is represented by x.
According to the problem, the measure of one angle is 30 degrees less than one-third the measure of its supplement.
The supplement of the angle can be found by subtracting the angle from 180 degrees since the sum of two supplementary angles is 180 degrees.
So, the supplement of the angle is represented by 180 - x.
The problem states that the measure of one angle is 30 degrees less than one-third the measure of its supplement.
This can be represented as x = (1/3)(180 - x) - 30.
Now, let's solve the equation:
x = (1/3)(180 - x) - 30
Multiplying both sides by 3 to eliminate the fraction:
3x = 180 - x - 90
Adding x to both sides:
4x = 180 - 90
4x = 90
Dividing both sides by 4:
x = 90/4
x = 22.5
So one of the angles is 22.5 degrees.
To find the other angle, we subtract the value of the first angle from 180 degrees since the sum of two supplementary angles is 180 degrees.
The other angle is 180 - 22.5 = 157.5 degrees.
Therefore, the two angles are 22.5 degrees and 157.5 degrees.
To solve this problem, we first need to recall that supplementary angles add up to 180 degrees. Let's denote one angle as 'x' and its supplement as '180 - x' (since their measures add up to 180 degrees).
According to the problem, the measure of one angle is 30 degrees less than one-third the measure of its supplement. Mathematically, we can write this as:
x = (1/3)(180 - x) - 30
Now, let's solve for x by simplifying the equation:
Multiply both sides of the equation by 3 to eliminate the fraction:
3x = 180 - x - 90
Combine like terms:
3x + x = 90
4x = 90
Divide both sides of the equation by 4 to isolate x:
x = 90 / 4
x = 22.5
Now, we can find the measure of the other angle by subtracting x from 180:
180 - x = 180 - 22.5 = 157.5
Therefore, the two angles are 22.5 degrees and 157.5 degrees.
If one angle = x, the other = 1/3x-30º
x + (1/3x-30º) = 180º
Solve for x.