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. Write an equation
Based on the Triangle Angle Sum Theorem, we know that the sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, the sum of the measures of the acute angles is:
(2x+6) + (3x-26) = 180
Simplify the equation:
2x + 6 + 3x - 26 = 180
5x - 20 = 180
5x = 200
x = 40
Now, we can find the measures of the acute angles:
2x + 6 = 2(40) + 6 = 80 + 6 = 86 degrees
3x - 26 = 3(40) - 26 = 120 - 26 = 94 degrees
Therefore, the measures of the missing angles are 86 degrees and 94 degrees.