Two angles are complementary. One angle is ten less than three times the other angle. Find the measure of both angles.
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To find the measure of the two angles, let's assign variables. Let's say the measure of one angle is x degrees.
According to the problem, the other angle is ten less than three times the first angle. So, the measure of the other angle can be represented as 3x - 10 degrees.
Since the two angles are complementary, the sum of their measures will be 90 degrees.
Therefore, we can write an equation based on this information:
x + (3x - 10) = 90
Now, let's solve this equation to find the value of x:
4x - 10 = 90
4x = 90 + 10
4x = 100
x = 25
Now that we know the value of x, we can substitute it back into one of the expressions to find the measure of the other angle:
3x - 10 = 3 * 25 - 10 = 75 - 10 = 65
So, the measure of the two angles is 25 degrees and 65 degrees, respectively.