Use the triangle angle sum theorem to find the measures of the angles for the triangle in the diagram
angles in triangle: 5x + 4, 4x + 14, 6x + - 3)
A) 59, 63, and 48
B) 57, 54, and 69
C) 59, 58, and 63
D) 54, 44, and 82
To use the triangle angle sum theorem, we need to set up the equation:
5x + 4 + 4x + 14 + 6x + (-3) = 180
Combining like terms, we get:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now, we can substitute this value back into the expressions for the angles:
Angle 1 = 5(11) + 4 = 59
Angle 2 = 4(11) + 14 = 58
Angle 3 = 6(11) - 3 = 63
Therefore, the measures of the angles are 59, 58, and 63.
The correct answer is C) 59, 58, and 63.