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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)
The Triangle Angle Sum Theorem states that the sum of the angles in any triangle is equal to 180 degrees.
Let's denote the missing angle as y. We have two given angles: 2x+6 degrees and 3x-26 degrees.
Using the Triangle Angle Sum Theorem, we can write the equation:
(2x+6) + (3x-26) + y = 180
Combining like terms:
5x - 20 + y = 180
Now, let's solve for y:
y = 180 - 5x + 20
y = 200 - 5x
So, the measure of the missing angle, y, is 200 - 5x degrees.