The measures of two supplementary angles are (10X-25) and (15X+50). Find the measure of the angles
review what supplementary angles are, then solve
10x-25 + 15x+50 = 180
Now that you have x, evaluate the two angles.
To find the measure of the angles, we need to set up an equation based on the fact that the two angles are supplementary, i.e., their sum is 180 degrees.
Let's denote the measure of the first angle as A = (10X - 25) and the measure of the second angle as B = (15X + 50).
According to the supplementary angle theorem, we have the equation:
A + B = 180
Substituting the values of A and B, we get:
(10X - 25) + (15X + 50) = 180
Now, let's solve the equation to find the value of X, which represents a proportionate relationship between the measures of the angles.
Combine like terms:
10X + 15X - 25 + 50 = 180
25X + 25 = 180
Subtract 25 from both sides:
25X = 155
Divide both sides by 25:
X = 6.2
Now that we have the value of X, we can substitute it back into either A or B to find the measures of the angles.
Let's substitute X = 6.2 into A:
A = (10X - 25) = (10 * 6.2 - 25) = 62 - 25 = 37
Therefore, the measure of the first angle is 37 degrees.
Now, let's substitute X = 6.2 into B:
B = (15X + 50) = (15 * 6.2 + 50) = 93 + 50 = 143
Therefore, the measure of the second angle is 143 degrees.
In conclusion, the measure of the angles are 37 degrees and 143 degrees.