A right triangle has acute angles measuring (2x + 6) degrees and (3x + 14) degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the Triangle
The Triangle Angle Sum Theorem states that the sum of the interior angles in a triangle is equal to 180 degrees. Therefore, we can write the equation:
(2x + 6) + (3x + 14) + m = 180
Simplifying, we have:
5x + 20 + m = 180
Subtracting 20 from both sides, we get:
5x + m = 160
We know that the angle measures must be positive, so m must be greater than 0. Since the triangle is a right triangle, one of the angles must be 90 degrees. Therefore, we can set up the equation:
5x + m = 90
Solving these two equations as a system, we find:
5x + m = 90
5x + m = 160
Subtracting the first equation from the second equation, we get:
0 = 70
This equation has no solution, which means there is no right triangle with angles measuring (2x + 6) and (3x + 14) degrees.