The problem asks for the measure of $\angle JIG$ in the triangle, and the diagram shows a triangle with sides labeled with algebraic expressions.

From the diagram:

• $\overline{GI} = 3x + 2$
• $\overline{IJ} = 13x - 3$
• $\angle GHI = 55^\circ$

However, to find the measure of $\angle JIG$, we can use the fact that the sum of the angles in any triangle is $180^\circ$.

Steps to solve:

1. Let's assume the angles at each vertex:

   • $\angle GHI = 55^\circ$ (given)
   • $\angle JIG = y$ (which we need to find)
   • $\angle GJI = z$

2. To find $\angle JIG$, we need to use the properties of the triangle and the angle sum theorem: $\angle GHI + \angle JIG + \angle GJI = 180^\circ$ Substituting the known value: $55^\circ + y + z = 180^\circ$ Simplifying: $y + z = 125^\circ$

Unfortunately, we don't have enough information to calculate $y$ or $z$ directly from this. Are there any additional conditions or angle relationships provided that we might use?

Feel free to ask for clarification, and I'll be happy to help!

Expanding questions:

1. Do you know the relationship between the sides and angles of this triangle?
2. Can we assume any other angle relationships or properties of the triangle?
3. Should we solve for the value of $x$ using the equation $3x + 2 = 13x - 3$ to get side lengths?
4. Is this a specific type of triangle (e.g., isosceles or right-angled)?
5. Are you familiar with using the Law of Sines or Cosines to solve for angles in non-right triangles?

Tip: Always use the sum of angles in a triangle when solving for missing angles.