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.(4 points) simplify asmswer
Sum of angles in a triangle = 180 degrees
Given angles:
2x + 6 degrees and 3x - 26 degrees
Sum of angles: (2x + 6) + (3x - 26) = 180
2x + 6 + 3x - 26 = 180
5x - 20 = 180
5x = 200
x = 40
Now, substitute x back into the given angles to find their measures:
2x + 6 = 2(40) + 6 = 86 degrees
3x - 26 = 3(40) - 26 = 114 degrees
Therefore, the angles of the right triangle are:
86 degrees, 114 degrees, and 90 degrees.