4. Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with the angle measures of (x - 30)°, (2x + 6)°, and (2x + 4)°.
The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.
So, we can set up an equation using the angle measures given:
(x - 30) + (2x + 6) + (2x + 4) = 180
Combine like terms:
5x - 20 = 180
Add 20 to both sides:
5x = 200
Divide by 5:
x = 40
Now we can substitute this value back into the angle measures to find the largest angle:
2x + 6 = 2(40) + 6 = 80 + 6 = 86 degrees
Therefore, the largest angle in the triangle is 86 degrees.