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 180 degrees.
So, we can set up an equation to find the missing angle:
(2x+6) + (3x-26) + missing angle = 180
Combine like terms:
5x - 20 + missing angle = 180
Add 20 to both sides:
5x + missing angle = 200
Now, we know that the missing angle in a right triangle (the right angle) measures 90 degrees. So we can substitute that in:
5x + 90 = 200
Subtract 90 from both sides:
5x = 110
Divide by 5:
x = 22
Now plug x back into the expressions for the acute angles:
2(22) + 6 = 50
3(22) - 26 = 56
Therefore, the acute angles measure 50 degrees and 56 degrees.