To find the measure of the angles of the triangle, we use the fact that the sum of the angles in a triangle is always 180 degrees.
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, let's solve for \( x \):
\[ 3x = 180 - 60 \] \[ 3x = 120 \] \[ x = 40 \]
Now, we can find the actual 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 measures of the angles are \( 50^\circ \), \( 60^\circ \), and \( 70^\circ \).
Therefore, the smallest angle is \( 50^\circ \).
The correct response is 50°.