To solve for the smallest angle in the triangle, we first need to find the value of \(x\) using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle equals 180°.
The angles are given as:
- Angle 1: \((x + 10)^\circ\)
- Angle 2: \((x + 20)^\circ\)
- Angle 3: \((x + 30)^\circ\)
We can set up the equation like this: \[ (x + 10) + (x + 20) + (x + 30) = 180 \]
Combining like terms gives us: \[ 3x + 60 = 180 \]
Next, we solve for \(x\) by subtracting 60 from both sides: \[ 3x = 120 \]
Now, divide by 3: \[ x = 40 \]
Now we can find the measures of the angles:
- 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 of the triangle are \(50^\circ\), \(60^\circ\), and \(70^\circ\).
Thus, the smallest angle is: \[ \boxed{50^\circ} \]