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)
Three setences
1 answer
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.