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. Write an equation

Answer 1

Based on the Triangle Angle Sum Theorem, we know that the sum of the measures of the angles in a triangle is always 180 degrees.

Therefore, the sum of the measures of the acute angles is:

(2x+6) + (3x-26) = 180

Simplify the equation:

2x + 6 + 3x - 26 = 180
5x - 20 = 180
5x = 200
x = 40

Now, we can find the measures of the acute angles:

2x + 6 = 2(40) + 6 = 80 + 6 = 86 degrees
3x - 26 = 3(40) - 26 = 120 - 26 = 94 degrees

Therefore, the measures of the missing angles are 86 degrees and 94 degrees.