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)

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always equal to 180 degrees.

Let's denote the missing angle as y.

According to the information given, we have the following equation:
(2x + 6) + (3x - 26) + y = 180

Simplifying the equation, we have:
5x - 20 + y = 180

Now, let's solve for y:
y = 180 - 5x + 20
y = -5x + 200

So, the measure of the missing angle is -5x + 200 degrees.

Answer 2

simplifiy