The measure of one angle is 15 degrees more than half the measure of its complement. Find the measure of the two angles.
A = Compliment = X Deg.
B = (X/2 + 15) Deg.
The sum of complimentary angles = 90 Deg.
X + (X/2+15) = 90 Deg.
Multiply both sides by 2:
2x + x + 30 = 180.
3x = 180 - 30 = 150.
X = 150 / 3 = 50 Deg.
x/2 + 15 = 50/2 + 15 = 40 Deg.
To solve this problem, we need to translate the given information into equations and then solve them simultaneously.
Let's assume that the measure of one angle is represented by 'x' degrees.
The measure of its complement (the other angle) can be represented by 90 - x degrees since the sum of an angle and its complement is always 90 degrees.
According to the problem, one angle is 15 degrees more than half the measure of its complement. In equation form, this can be written as:
x = (1/2)(90 - x) + 15
To solve this equation, we first simplify the right side:
x = 45 - (1/2)x + 15
Next, we combine like terms:
x = (45 + 15) - (1/2)x
Now, we simplify the right side:
x = 60 - (1/2)x
Next, we multiply both sides of the equation by 2 to eliminate the fraction:
2x = 120 - x
Now, we add 'x' to both sides:
2x + x = 120
Finally, we combine like terms:
3x = 120
To find the value of 'x', we divide both sides of the equation by 3:
x = 120/3
x = 40
So, the measure of one angle is 40 degrees and the measure of its complement is 90 - 40 = 50 degrees.