To find the largest angle in the triangle with angle measures \((x−20)°\), \((3x+3)°\), and \((2x−7)°\), we first apply the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle must equal \(180°\).
We can set up the equation based on the given angles:
\[ (x - 20) + (3x + 3) + (2x - 7) = 180 \]
Now, let's combine like terms:
\[ x - 20 + 3x + 3 + 2x - 7 = 180 \]
\[ (1x + 3x + 2x) + (-20 + 3 - 7) = 180 \]
This simplifies to:
\[ 6x - 24 = 180 \]
Next, we add \(24\) to both sides:
\[ 6x = 204 \]
Dividing both sides by \(6\) gives:
\[ x = 34 \]
Now, we can substitute \(x\) back into the expressions for each angle to find the measures of the angles:
- For the angle \((x - 20)°\):
\[ x - 20 = 34 - 20 = 14° \]
- For the angle \((3x + 3)°\):
\[ 3x + 3 = 3(34) + 3 = 102 + 3 = 105° \]
- For the angle \((2x - 7)°\):
\[ 2x - 7 = 2(34) - 7 = 68 - 7 = 61° \]
Now we have the measures of the angles:
- \((x - 20)° = 14°\)
- \((3x + 3)° = 105°\)
- \((2x - 7)° = 61°\)
The largest angle among these is:
\[ 105° \]
Thus, the largest angle in the triangle is \(\boxed{105°}\).
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