To solve for $x$ in the triangle $\triangle DEC$, let’s analyze the given information:

1. Labeling the Triangle:
   • $DE = 5x + 8$
   • $DC = 6x + 8$
   • Angle $DCE = 82^\circ$

Since we have a triangle and no right angles indicated, we'll consider the possibility of using the Law of Sines or Law of Cosines if more angles or side relationships were given. However, without additional angle information besides $82^\circ$, it's not immediately clear if these rules can apply directly without more information.

Steps to Determine $x$:

If this is a right triangle or an isosceles triangle, further details like other angles or side lengths would help. The angle $82^\circ$ alone does not provide enough to solve directly for $x$.

Could you clarify if there are additional known details about triangle $DEC$, such as:

• Whether it's a right triangle.
• Any other angle measures.

Otherwise, solving for ( x \