Let's analyze the triangles in the image to determine whether they are similar.

Step 1: Identify Known Angles

• In ΔLMN:

  • ∠M = 115°
  • ∠N = 21°
  • Using the angle sum property of a triangle, we can find the missing angle ∠L: $\angle L = 180^\circ - 115^\circ - 21^\circ = 44^\circ.$

• In ΔPQR:

  • ∠P = 49°
  • ∠R = 21°
  • Similarly, find the missing angle ∠Q: $\angle Q = 180^\circ - 49^\circ - 21^\circ = 110^\circ.$

Step 2: Compare Corresponding Angles

For two triangles to be similar, their corresponding angles must be equal.

• Compare:
  • ∠N (21°) = ∠R (21°) ✔
  • ∠L (44°) ≠ ∠P (49°) ✖
  • ∠M (115°) ≠ ∠Q (110°) ✖

Since not all corresponding angles are equal, ΔLMN is not similar to ΔPQR.

Conclusion

The correct statement is:

• "ΔLMN is not similar to ΔPQR."

Would you like further clarification or have additional questions?

Here are 5 related questions for practice:

1. What is the Angle Sum Property of a triangle?
2. How do you determine if two triangles are similar by the AA (Angle-Angle) criterion?
3. Can triangles with equal sides but different angles be similar?
4. What other criteria can we use to test triangle similarity (e.g., SSS, SAS)?
5. How does similarity differ from congruence in triangles?

Tip: Always double-check that corresponding angles match when testing for similarity between triangles!