The problem states that a triangle has angle measures of $(x+3)^\circ$, $(5x-8)^\circ$, and $(2x+1)^\circ$. The task is to find the measure of the smallest angle of the triangle in degrees.

1. Problem Description

The problem states that a triangle has angle measures of $(x+3)^\circ$, $(5x-8)^\circ$, and $(2x+1)^\circ$. The task is to find the measure of the smallest angle of the triangle in degrees.

2. Solution Steps

The sum of the angles in a triangle is $180^\circ$. Therefore, we have the equation:

$(x+3) + (5x-8) + (2x+1) = 180$.

Combine like terms:

$8x - 4 = 180$.

Add 4 to both sides:

$8x = 184$.

Divide by 8:

$x = \frac{184}{8} = 23$.

Now we can find the measures of the three angles:

Angle 1: $x+3 = 23+3 = 26^\circ$.

Angle 2: $5x-8 = 5(23)-8 = 115-8 = 107^\circ$.

Angle 3: $2x+1 = 2(23)+1 = 46+1 = 47^\circ$.

The three angles are $26^\circ$, $107^\circ$, and $47^\circ$.

The smallest angle is $26^\circ$.

3. Final Answer

The measure of the smallest angle of the triangle is $26^\circ$.