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

Answer 1

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.