To find the measures of the angles in triangle ABC, we can set up the equation using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees.
Given:
- Angle A = \(4x + 14\)
- Angle B = \(5x + 4\)
- Angle C = \(6x - 3\)
We can set up the equation:
\[ (4x + 14) + (5x + 4) + (6x - 3) = 180 \]
Combining like terms:
\[ 4x + 5x + 6x + 14 + 4 - 3 = 180 \]
This simplifies to:
\[ 15x + 15 = 180 \]
Now, subtract 15 from both sides:
\[ 15x = 165 \]
Now, divide by 15:
\[ x = 11 \]
Next, we can find the measure of each angle by substituting \(x\) back into the expressions for the angles:
-
Angle A: \[ 4x + 14 = 4(11) + 14 = 44 + 14 = 58° \]
-
Angle B: \[ 5x + 4 = 5(11) + 4 = 55 + 4 = 59° \]
-
Angle C: \[ 6x - 3 = 6(11) - 3 = 66 - 3 = 63° \]
Now, we have:
- Angle A = 58°
- Angle B = 59°
- Angle C = 63°
Thus, the angles of the triangle are 58°, 59°, and 63°.
The correct response choice is:
59°, 58°, and 63°