To solve the problem, we need to analyze the given triangle diagram and the relationships between the angles.

Analysis:

1. Triangle DEF is the larger triangle, and triangle GHI is formed by connecting the midpoints of triangle DEF.

   • This makes triangle GHI a midsegment triangle, meaning its sides are parallel to the sides of the larger triangle, and its angles correspond proportionally to the angles of DEF.

2. From the diagram:

   • $\angle F = 47^\circ$,
   • $\angle E = 62^\circ$,
   • $\angle D = 71^\circ$.

3. Triangle DEF is a triangle, so the sum of its interior angles is: $\angle D + \angle E + \angle F = 180^\circ.$

4. Focus on $\angle DIG$:

   • $\angle DIG$ is located within triangle GHI. Since triangle GHI is the midsegment triangle, its angles are equal to the angles of triangle DEF.

Thus: $m\angle DIG = \angle D = 71^\circ.$

Final Answer:

$m\angle DIG = 71^\circ$

Would you like a breakdown of midsegment triangle properties or have any other questions?

Related Questions:

1. How can you prove that triangle GHI is a midsegment triangle?
2. What is the relationship between the sides of triangle DEF and triangle GHI?
3. Why is the sum of the angles in any triangle always $180^\circ$?
4. How can you verify that the given angles form a valid triangle?
5. What are other applications of the midsegment theorem in geometry?

Tip:

Remember, in midsegment triangles, the corresponding angles remain unchanged, and the sides are always half the length of the parallel sides in the larger triangle.