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 angle of the triangle
The sum of the measures of the angles in a triangle is always 180 degrees.
So, we have:
(2x+6) + (3x-26) + Missing Angle = 180
Combine like terms:
5x - 20 + Missing Angle = 180
Add 20 to both sides:
5x + Missing Angle = 200
To find the measure of the missing angle, we need to substitute back for the expressions:
Missing Angle = 200 - (2x+6) - (3x-26)
Missing Angle = 200 - 2x - 6 - 3x + 26
Missing Angle = 200 - 2x -3x + 26 - 6
Missing Angle = -5x + 220
Therefore, the measure of the missing angle in the triangle is -5x + 220 degrees.