To find the measures of each angle in the triangle, we can apply the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
The angles of the triangle are given as:
- Angle 1: \(5x - 1\) degrees
- Angle 2: \(8x + 5\) degrees
- Angle 3: \(4x + 6\) degrees
Using the Triangle Angle Sum Theorem, we set up the equation:
\[ (5x - 1) + (8x + 5) + (4x + 6) = 180 \]
Now, let's combine the like terms:
\[ 5x + 8x + 4x - 1 + 5 + 6 = 180 \]
This simplifies to:
\[ 17x + 10 = 180 \]
Now, subtract 10 from both sides:
\[ 17x = 170 \]
Next, divide by 17 to solve for \(x\):
\[ x = 10 \]
Now that we have \(x\), we can substitute it back into the expressions for each angle:
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For Angle 1: \[ 5x - 1 = 5(10) - 1 = 50 - 1 = 49 \text{ degrees} \]
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For Angle 2: \[ 8x + 5 = 8(10) + 5 = 80 + 5 = 85 \text{ degrees} \]
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For Angle 3: \[ 4x + 6 = 4(10) + 6 = 40 + 6 = 46 \text{ degrees} \]
Thus, the measures of the angles in the triangle are:
- Angle 1: \(49^\circ\)
- Angle 2: \(85^\circ\)
- Angle 3: \(46^\circ\)
Given the choices, the correct response is:
46°, 49°, and 85°.