To find the measure of the smallest angle in the triangle with angles measuring (x + 10)°, (x + 20)°, and (x + 30)°, we first need to find the value of \( x \) using the fact that the sum of the angles in a triangle is 180°.
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Set up the equation: \[ (x + 10) + (x + 20) + (x + 30) = 180 \]
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Simplify the left side: \[ 3x + 60 = 180 \]
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Subtract 60 from both sides: \[ 3x = 120 \]
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Divide by 3: \[ x = 40 \]
Now that we have \( x \), we can find the measures of the angles:
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First angle: \[ x + 10 = 40 + 10 = 50° \]
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Second angle: \[ x + 20 = 40 + 20 = 60° \]
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Third angle: \[ x + 30 = 40 + 30 = 70° \]
The angles of the triangle are 50°, 60°, and 70°.
The smallest angle is: \[ \boxed{50°} \]