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 angle of the triangle.
The triangle angle sum theorem states that the sum of the angles in a triangle is 180 degrees.
Since the triangle is a right triangle, one of the angles is 90 degrees.
Let's use the triangle angle sum theorem to find the measures of the missing angles:
(2x + 6) + (3x - 26) + 90 = 180
Combining like terms:
5x - 20 + 90 = 180
5x + 70 = 180
Subtracting 70 from both sides:
5x = 110
Dividing both sides by 5:
x = 22
Now we can find the measures of the missing angles:
First angle: 2x + 6 = 2(22) + 6 = 44 + 6 = 50 degrees
Second angle: 3x - 26 = 3(22) - 26 = 66 - 26 = 40 degrees
The measure of the missing angle is 180 - (90 + 50 + 40) = 180 - 180 = 0 degrees
Therefore, the missing angle of the triangle is 0 degrees.