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. Make it short but correct.(4 points)
make it shorter
The third angle of the triangle can be found using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180 degrees.
Therefore, the third angle measures (2x + 6) + (3x - 26) = 5x - 20 degrees.
Since it is a right triangle, one of the angles measures 90 degrees.
To find the third angle, we can set up an equation:
90 + (2x + 6) + (3x - 26) = 180
Solving for x, we get x = 28.
Substitute x = 28 back into the third angle formula: 5(28) - 20 = 120 degrees.
Therefore, the missing angles of the right triangle are 120 degrees and 60 degrees.