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. Make it short but correct.(4 points)

Answer 1

The third angle of the triangle can be found using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180 degrees.

Therefore, the third angle measures (2x + 6) + (3x - 26) = 5x - 20 degrees.

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

To find the third angle, we can set up an equation:

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

Solving for x, we get x = 28.

Substitute x = 28 back into the third angle formula: 5(28) - 20 = 120 degrees.

Therefore, the missing angles of the right triangle are 120 degrees and 60 degrees.

Answer 2

Shorter

Answer 3

The third angle of the right triangle is 50 degrees, and the missing angles are 50 degrees and 90 degrees.

Answer 4

make it shorter