SOLUTION: The sum of the measures of the two acute angles in a right triangle is 90 degrees and their difference is 16. Find the measure of each angle.

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Question 1124935: The sum of the measures of the two acute angles in a right triangle is 90 degrees and their difference is 16. Find the measure of each angle.
Found 3 solutions by josgarithmetic, math_helper, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the measures of the two acute angles in a right triangle is 90 degrees and their difference is 16. Find the measure of each angle.
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One angle is x
The other is then 90-x

x = (90-x)-16
2x = 74
x = 37
90-x = 53
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Ans: The two angles are +highlight%28+53%5Eo+%29+ and +highlight%28+37%5Eo+%29+
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"The sum of the measures of the two acute angles in a right triangle is 90 degrees" <—<<< always true for a right triangle.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If an algebraic solution is not required, here is a quick way to solve this problem using logical reasoning and a bit of simple arithmetic.

The sum of the two angles is 90 degrees.
If they were each 45 degrees, there would be no difference between their measures.
To get a difference of 16 degrees between the two angles, you need to add 8 degrees to one of the 45 degree angles and subtract 8 from the other.

Answer: 45+8=53 and 45-8 = 37.