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.

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(39617)   (Show Source): You can put this solution on YOUR website!

37 and 53
Answer by math_helper(2461)   (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.
===========================
One angle is x
The other is then 90-x

x = (90-x)-16
2x = 74
x = 37
90-x = 53
��
Ans: The two angles are and
��
"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)   (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.
RELATED QUESTIONS
The sum of the measures of the two acute angles in a right triangle is 90 and their... (answered by jim_thompson5910)
what is the sum of the measures of the two acute angles of a right... (answered by stanbon)
The measures of the two acute angles of a right triangle differ by 18 degrees. What are... (answered by RAY100)
the measures of the two acute angles of a right triangle differ by 15 degrees. What are... (answered by solver91311)
An acute angle is an angle whose measure is less than 90 degrees. A right triangle is a... (answered by stanbon)
In the right triangle, the ratio of the measures of the two acute angles is 4:1. What is... (answered by stanbon)
in the right triangle, the ratio of the measures of the two acute angles is 4:1. what is... (answered by checkley77)
In a right triangle, one of the acute angles is fourteen times as large as the other... (answered by checkley77)
If the two acute angles of a right triangle have measures (2x-11)degrees and... (answered by josgarithmetic)