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) written in a super easy simple sentence

Answer 1

In a right triangle, the angles add up to 180 degrees, so we know that the two acute angles (2x + 6) and (3x - 26) plus the right angle (90 degrees) must equal 180 degrees.

Setting up the equation:

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

Simplifying this gives:

5x - 20 + 90 = 180,

which simplifies to:

5x + 70 = 180.

Subtracting 70 from both sides results in:

5x = 110.

Dividing by 5 gives:

x = 22.

Now substitute x back into the angle expressions:

1. First angle: 2(22) + 6 = 44 + 6 = 50 degrees.
2. Second angle: 3(22) - 26 = 66 - 26 = 40 degrees.

So the triangle's angles are 50 degrees, 40 degrees, and 90 degrees.