To find the measures of the angles in the triangle, we can use the fact that the sum of the angles in a triangle is always 180°. The angles given are \(x^\circ\), \(2x^\circ\), and \((3x - 12)^\circ\). We can set up the equation:
\[ x + 2x + (3x - 12) = 180 \]
Now, let's simplify the left side of the equation:
\[ x + 2x + 3x - 12 = 180 \] \[ 6x - 12 = 180 \]
Next, we'll add 12 to both sides:
\[ 6x = 180 + 12 \] \[ 6x = 192 \]
Now, we can divide both sides by 6 to solve for \(x\):
\[ x = \frac{192}{6} \] \[ x = 32 \]
Now we can find each angle:
- The first angle is \(x = 32^\circ\).
- The second angle is \(2x = 2(32) = 64^\circ\).
- The third angle is \((3x - 12) = 3(32) - 12 = 96 - 12 = 84^\circ\).
Thus, the measures of the angles in the triangle are:
- \(32^\circ\)
- \(64^\circ\)
- \(84^\circ\)
In summary, the measures of the angles are \(32^\circ\), \(64^\circ\), and \(84^\circ\).
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