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)

Answer 1

Since it is a right triangle, one of the angles is equal to 90 degrees.

Let's use the Triangle Angle Sum Theorem: the sum of the angles in a triangle is equal to 180 degrees.

So, we have:
2x+6 + 3x-26 + 90 = 180
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22

Now we can find the measures of the missing angles:
2(22) + 6 = 50 degrees
3(22) - 26 = 40 degrees

Therefore, the measures of the missing angles are 50 degrees and 40 degrees.