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)°
According to the Triangle Angle Sum Theorem, the sum of the measures of the angles in a triangle is 180°.
So, we can set up an equation:
(x-30)° + (2x+6)° + (2x+4)° = 180°
Combining like terms:
x - 30 + 2x + 6 + 2x + 4 = 180
5x - 20 = 180
Adding 20 to both sides:
5x = 200
Dividing both sides by 5:
x = 40
Now, we can substitute the value of x back into the angle measures to find their values:
The first angle: (x-30)° = (40-30)° = 10°
The second angle: (2x+6)° = (2*40+6)° = 86°
The third angle: (2x+4)° = (2*40+4)° = 84°
Therefore, the largest angle in the triangle has a measure of 86°.