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) write this out sounding like a 7th grader
Alright, so we know that the Triangle Angle Sum Theorem says that the sum of all angles in a triangle is 180 degrees. In this right triangle, we have two of the angles: 2x+6 degrees and 3x-26 degrees.
To find the missing angle, we add the two given angles together and subtract the sum from 180 degrees to find the third angle.
So,
(2x+6) + (3x-26) = 180
5x - 20 = 180
5x = 200
x = 40
Now that we have found the value of x, we can substitute it back into the expressions for the given angles to find their measures.
2(40) + 6 = 86 degrees
3(40) - 26 = 94 degrees
Therefore, the missing angle measures 180 - 86 - 94 = 0 degrees.