A right triangle has acute angles measuring 2x+6 degrees and 3x-26 degrees. Use the triangle angle sum theorem to find the measure of the missing angles of the triangle
The sum of the measures of the angles in any triangle is always 180 degrees.
Let the missing angle be y degrees.
Therefore, we have the equation:
2x + 6 + 3x - 26 + y = 180
Combining like terms:
5x - 20 + y = 180
Rearranging the equation:
5x + y = 200
Since we know that x is a positive integer, we can find the possible values of x that make the equation true.
For x = 30:
5(30) + y = 200
150 + y = 200
y = 200 - 150
y = 50
Thus, the missing angle in the triangle is 50 degrees.