To find the measure of the smallest angle in the triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Given the angles in the triangle, we have:
- Top angle = 96 degrees
- Bottom left angle = \(2x\)
- Bottom right angle = \(x + 12\)
We can set up the equation as follows:
\[ 96 + 2x + (x + 12) = 180 \]
Now, simplify the equation:
\[ 96 + 2x + x + 12 = 180 \] \[ 3x + 108 = 180 \]
Next, isolate \(3x\):
\[ 3x = 180 - 108 \] \[ 3x = 72 \]
Now, solve for \(x\):
\[ x = \frac{72}{3} = 24 \]
Now we can find the measures of the bottom left and bottom right angles:
-
Bottom left angle (\(2x\)): \[ 2x = 2 \cdot 24 = 48 \text{ degrees} \]
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Bottom right angle (\(x + 12\)): \[ x + 12 = 24 + 12 = 36 \text{ degrees} \]
Now, we have the measures of all angles:
- Top angle = 96 degrees
- Bottom left angle = 48 degrees
- Bottom right angle = 36 degrees
Finally, the smallest angle in the triangle is:
\[ \text{Smallest angle} = 36 \text{ degrees} \]
Therefore, the measure of the smallest angle of the triangle is \( \boxed{36} \) degrees.
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