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)
To find the missing angles of the right triangle, we can first use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. The two given acute angles add up to 2x+6 + 3x-26 = 5x-20 degrees. Since it is a right triangle, one angle is always 90 degrees. To find the third angle, we can set up the equation 5x-20 + 90 = 180 and solve for x, which gives x = 22. Substituting x back into the expressions for the given angles, we find that the acute angles measure 50 degrees and 40 degrees.
