To find the measure of the smallest angle in the triangle, we start by using the fact that the sum of the angles in a triangle is \(180^\circ\).
Given the angles:
- Angle 1: \( (x + 10)^\circ \)
- Angle 2: \( (x + 20)^\circ \)
- Angle 3: \( (x + 30)^\circ \)
We can set up the equation:
\[ (x + 10) + (x + 20) + (x + 30) = 180 \]
Combining like terms:
\[ 3x + 60 = 180 \]
Now, subtract 60 from both sides:
\[ 3x = 120 \]
Now, divide by 3:
\[ x = 40 \]
Now we can find each angle:
- Angle 1: \( x + 10 = 40 + 10 = 50^\circ \)
- Angle 2: \( x + 20 = 40 + 20 = 60^\circ \)
- Angle 3: \( x + 30 = 40 + 30 = 70^\circ \)
The angles are \(50^\circ\), \(60^\circ\), and \(70^\circ\). The smallest angle is:
\[ \text{Smallest angle} = 50^\circ \]
Therefore, the measure of the smallest angle is 50°.
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