1. The problem states that the sum of the angles in a triangle is 180 degrees. 2. The angles given are $32c + 5$, $24c$, and $c + 32$ degrees. 3. Write the equation for the sum of angles: $$ (32c + 5) + 24c + (c + 32) = 180 $$ 4. Combine like terms: $$ 32c + 24c + c + 5 + 32 = 180 $$ $$ 57c + 37 = 180 $$ 5. Subtract 37 from both sides: $$ 57c + \cancel{37} - \cancel{37} = 180 - 37 $$ $$ 57c = 143 $$ 6. Divide both sides by 57: $$ \frac{57c}{\cancel{57}} = \frac{143}{57} $$ $$ c = \frac{143}{57} \approx 2.5 $$ 7. The value of $c$ rounded to the nearest tenth is $2.5$.