One of two supplementary angles measures 65 degrees more than half the other. Find each angle.
x + (x/2 + 65) = 180
65(x+2)=90
To solve this problem, let's denote one of the angles as x and the other angle as y.
We are given that the two angles are supplementary, which means their sum is 180 degrees. Therefore, we can write the equation:
x + y = 180
We are also given that one of the angles measures 65 degrees more than half the other. We can write this as an equation as well:
x = (1/2)y + 65
Now we have a system of equations. We can solve it by substituting the second equation into the first equation:
(1/2)y + 65 + y = 180
Simplifying this equation:
(3/2)y + 65 = 180
Subtracting 65 from both sides:
(3/2)y = 115
To solve for y, we can multiply both sides by 2/3:
y = (2/3) * 115 = 76.67
Since the angles are supplementary, we can find the value of x by subtracting y from 180:
x = 180 - 76.67 = 103.33
Therefore, one angle measures approximately 76.67 degrees and the other angle measures approximately 103.33 degrees.