A night triangle has acule angles measuring 2x + 6 degrees and 3x-20 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the tnangle (4 points)

Answer 1

To find the measures of the missing angles of the triangle, we first need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

Let the measures of the two known angles be 2x + 6 and 3x - 20 degrees.

According to the Triangle Angle Sum Theorem:
(2x + 6) + (3x - 20) + (missing angle) = 180

Combine like terms:
5x - 14 + (missing angle) = 180

Now, solve for x:
5x - 14 + (missing angle) = 180
5x - 14 = 180 - (missing angle)
5x = 194 - missing angle
5x = 180 + missing angle
5x = 194

Divide both sides by 5:
x = 38.8

Now, substitute x back into the expressions of the known angles to find their measures:
2(38.8) + 6 = 83.6 degrees
3(38.8) - 20 = 96.4 degrees

Now, find the measure of the missing angle by plugging x back into the equation:
5(38.8) - 14 + (missing angle) = 180
194 - 14 + (missing angle) = 180
180 + (missing angle) = 180
(missing angle) = 0 degrees

Therefore, the missing angle of the triangle is 0 degrees.