A right triangle has acute angles measuring 2x + 6° and 3x - 26° using the triangle angle sum theorem to measure to find the measures of the missing angles of the triangle

Let's use the triangle angle sum theorem to find the measures of the missing angles.

In a triangle, the sum of all three angles is 180°.

So, we have:

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

Simplify the equation:

5x - 20 + ? = 180

Add 20 to both sides:

5x + ? = 200

Since the triangle is a right triangle, one of the angles is 90°.

Now we can substitute this information back into our equation:

5x + 90 = 200

Subtract 90 from both sides:

5x = 110

Divide by 5:

x = 22

Now we can find the measures of the missing angles:

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

Therefore, the measures of the missing angles are:
50°, 40°, and 90°.