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)
The sum of the angles in a triangle is always 180 degrees.
So, we have:
(2x+6) + (3x-26) + missing angle = 180 degrees
Combine like terms:
5x - 20 + missing angle = 180
Solve for missing angle:
missing angle = 180 - 5x + 20
Since we know the triangle is a right triangle, one angle is 90 degrees. Therefore:
(2x+6) + (3x-26) + 90 = 180
Combine like terms:
5x -20 + 90 = 180
5x + 70 = 180
5x =110
x = 22
Now, substitute x = 22 back into the missing angle equation:
missing angle = 180 - 5(22) + 20
missing angle = 180 - 110 + 20
missing angle = 90
Therefore, the measures of the missing angles of the triangle are 90 degrees each.