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.

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.

Let's use this theorem to find the measure of the third angle in the right triangle.

We know that one of the acute angles measures 2x+6 degrees and the other measures 3x−26 degrees.

So,

2x+6 + 3x−26 + 90 = 180

5x - 20 = 90

5x = 110

x = 22

Now we can find the measures of the missing angles:

2x+6 = 2(22)+6 = 50 degrees

3x−26 = 3(22)−26 = 40 degrees

Therefore, the measures of the missing angles of the right triangle are 40 degrees and 50 degrees.