SOLUTION: In a right triangle, one acute angle is twice the size of the other. What are their measures?

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Question 725409: In a right triangle, one acute angle is twice the size of the other. What are their measures?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The measures of all 3 angles in any triangle add up to 180%5Eo .
A right triangle has a right angle that measures 90%5Eo ,
so the measures of the other two angles must add up to 180%5Eo-90%5Eo=90%5Eo .
That means that the measure of each of those other angle will be less than 90%5Eo ,
so the other 2 angles are acute angles.
x= measure of the smaller acute angle (in degrees) and
2x= measure of the other acute angle (in degrees).
The sum of those 2 measures (in degrees) is
x%2B2x=90 --> 3x=90 --> 3x%2F3=90%2F3 --> highlight%28x=30%29
So 2x=2%2A30 --> highlight%282x=60%29
The acute angles measure highlight%2830%5Eo%29 and highlight%2860%5Eo%29 .