Final answer:
To find the smallest angle in a triangle with angles of 3(x)°, (2x - 13)°, and (5x + 3)°, calculate the value of x using the fact that the sum of angles in a triangle is 180 degrees, then determine each angle's measure. In this case, the smallest angle is 25°.
Step-by-step explanation:
The problem involves finding the measure of the smallest angle in a triangle. We know that in a triangle, the sum of all interior angles is always 180 degrees. The given triangle has angles with measures of 3(x)°, (2x - 13)°, and (5x + 3)°.
To find the value of x, we set up the equation: 3x + (2x - 13) + (5x + 3) = 180. Simplifying this, we get 10x - 10 = 180, which results in x = 19 when we solve for x. Plugging this value back into the expressions for each angle, we get the following measures: 57°, 25°, and 98°.
Therefore, the measure of the smallest angle in the triangle is 25°.