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

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Question 902741: The sum of the measures of the two acute angles in a right triangle is 90 and their difference is 16. find the measure of each angle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of angles is 90: x+y = 90
Difference is 16: x-y = 16 (this implies x > y)


x+y = 90
x-y = 16

Add the equations

x+y = 90
x-y = 16
--------
2x+0y = 106

So we have

2x = 106

x = 106/2

x = 53

Use this to find y

x+y = 90

53+y = 90

y = 90-53

y = 37

So the two angles are 53 degrees and 37 degrees.