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 Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Given that the acute angles of the right triangle measure 2x+6 degrees and 3x-26 degrees, we can set up the equation:
(2x+6) + (3x-26) + 90 = 180
Combine like terms:
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 = 44 degrees
Therefore, the missing angles of the right triangle are 50 degrees and 44 degrees.