A right triangle has acute angles measuring (2x+6) degrees and (3x+14) degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.

Answer 1

The sum of the angles in a triangle is 180 degrees. Therefore, we have the equation:

(2x+6) + (3x+14) + angle3 = 180

Simplifying the equation, we get:

5x + 20 + angle3 = 180

Subtracting 20 from both sides, we have:

5x + angle3 = 160

Since angle3 is the last missing angle, we can solve for it by subtracting the sum of the other two angles from 180:

angle3 = 180 - [(2x+6) + (3x+14)]

Simplifying:

angle3 = 180 - 2x - 6 - 3x - 14
angle3 = 160 - 5x

So, the measure of the missing angle (angle3) in the triangle is 160 - 5x degrees.