To find the measure of the smallest angle in the triangle with angles measuring (x+10)°, (x+20)°, and (x+30)°, we need to use the fact that the sum of the angles in a triangle is 180°.
- Set up the equation:
\[ (x + 10) + (x + 20) + (x + 30) = 180 \]
- Simplify the left side:
\[ 3x + 60 = 180 \]
- Subtract 60 from both sides:
\[ 3x = 120 \]
- Divide by 3:
\[ x = 40 \]
- Now, substitute \(x = 40\) back into the expressions for the angles:
- First angle: \(x + 10 = 40 + 10 = 50°\)
- Second angle: \(x + 20 = 40 + 20 = 60°\)
- Third angle: \(x + 30 = 40 + 30 = 70°\)
The smallest angle is \(50°\).
So the measure of the smallest angle is 50 degrees.
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