A right try 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 ty

Answer 1

Given that the triangle is a right triangle, one of the angles is a right angle and measures 90 degrees.

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

So, we can write the equation:

(2x + 6) + (3x - 26) + 90 = 180

Combining like terms:

5x - 20 + 90 = 180
5x + 70 = 180

Subtracting 70 from both sides:

5x = 110

Dividing by 5:

x = 22

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

2x + 6 = 2(22) + 6 = 44 + 6 = 50 degrees
3x - 26 = 3(22) - 26 = 66 - 26 = 40 degrees

Therefore, the two acute angles measure 50 degrees and 40 degrees.