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) simplify answer
The sum of the interior angles of a triangle is always 180 degrees.
So, we can write the equation:
(2x + 6) + (3x - 26) + missing angle = 180
Simplify the equation:
2x + 6 + 3x - 26 + missing angle = 180
5x - 20 + missing angle = 180
5x + missing angle = 200
To find the missing angle, subtract 5x from both sides:
missing angle = 200 - 5x
Now, we need to find the value of x by setting the sum of the three angles equal to 180 degrees:
(2x + 6) + (3x - 26) + (200 - 5x) = 180
5x - 20 + 200 - 5x = 180
180 = 180
This means that the value of x doesn't affect the sum of the angles, so the measures of the missing angles are:
2x + 6 = 2(0) + 6 = 6 degrees
3x - 26 = 3(0) - 26 = -26 degrees
missing angle = 200 - 5(0) = 200 degrees
Therefore, the measures of the missing angles are:
6 degrees, -26 degrees, and 200 degrees.