Short Answer
A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.
The sum of the three angles in a triangle is always 180 degrees.
So, we have:
(2x+6) + (3x-26) + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now, we can find the measures of the missing angles:
First acute angle: 2(22) + 6 = 50 degrees
Second acute angle: 3(22) - 26 = 60 degrees
Therefore, the measures of the missing angles are 50 degrees and 60 degrees.