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The swan below is composed of several triangles. Use the given information and the figure to find each angle measure. Note: Figure not drawn to scale.

Given: ΔABC is equilateral; DE¯¯¯¯¯¯¯¯≅CE¯¯¯¯¯¯¯¯≅EF¯¯¯¯¯¯¯¯
\overline{DE}\cong\overline{CE}\cong\overline{EF}; KO¯¯¯¯¯¯¯¯≅FO¯¯¯¯¯¯¯¯
\overline{KO}\cong\overline{FO}; JN¯¯¯¯¯¯¯¯≅JO¯¯¯¯¯¯¯
\overline{JN}\cong\overline{JO}; ∠BCD ≅ ∠BDC; CGF ≅ ∠CFG; ∠HKN ≅ ∠HNK; ΔGCF ≅ ΔGKF ≅ ΔJHM; ΔKFH ≅ ΔKLH

Triangular Swan Portfolio

Print the document so that you can write on it and mark the pictureshowin congruent sides​

(2 points)
1. m∠ABC =

2. m∠BCA =

3. m∠CAB =

4. m∠BCD =

5. m∠BDC =

6. m∠CBD =

Question 3
(2 points)
7. m∠EDC =

8. m∠ECD =

9. m∠CED =

10. m∠ECF =

11. m∠EFC =

12. m∠CEF =

Question 4
(2 points)
13. m∠CGF =

14. m∠CFG =

15. m∠GCF =

16. m∠KGF =

17. m∠KFG =

18. m∠GKF =

Question 5
(2 points)
19. m∠FKH =

20. m∠FHK =

21. m∠KFH =

22. m∠KHL =

23. m∠HKL =

24. m∠KLH =

Question 6
(2 points)
25. m∠HJM =

26. m∠HMJ =

27. m∠JHM =

28. m∠OFK =

29. m∠OKF =

30. m∠KOF =

Question 7
(2 points)
31. m∠HKN =

32. m∠HNK =

33. m∠OKN =

34. m∠JNO =

35. m∠JON =

36. m∠NJO =

1 answer

To calculate the angle measures based on the information provided, we will use the properties of congruent triangles and the fact that the angles in a triangle sum up to 180 degrees.

Given Information Recap:

  • ΔABC is equilateral
  • \( DE \cong CE \cong EF \)
  • \( KO \cong FO \)
  • \( JN \cong JO \)
  • \( ∠BCD \cong ∠BDC \)
  • \( CGF \cong ∠CFG \)
  • \( ∠HKN \cong ∠HNK \)
  • \( ΔGCF \cong ΔGKF \cong ΔJHM \)
  • \( ΔKFH \cong ΔKLH \)

Question 1

Since ΔABC is equilateral:

  1. \( m∠ABC = 60° \)
  2. \( m∠BCA = 60° \)
  3. \( m∠CAB = 60° \)

Question 2

Since \( DE \cong CE \cong EF \), triangle EDC is an equilateral triangle: 4. \( m∠BCD = 60° \) 5. \( m∠BDC = 60° \) 6. \( m∠CBD = 60° \)

Question 3

Based on the same reasoning (equilateral triangles): 7. \( m∠EDC = 60° \) 8. \( m∠ECD = 60° \) 9. \( m∠CED = 60° \) 10. \( m∠ECF = 60° \) 11. \( m∠EFC = 60° \) 12. \( m∠CEF = 60° \)

Question 4

For triangles GCF and KGF, which are congruent (as per the given information): 13. \( m∠CGF = 60° \) 14. \( m∠CFG = 60° \) 15. \( m∠GCF = 60° \) 16. \( m∠KGF = 60° \) 17. \( m∠KFG = 60° \) 18. \( m∠GKF = 60° \)

Question 5

In triangles KFH and KLH which are congruent: 19. \( m∠FKH = 60° \) 20. \( m∠FHK = 60° \) 21. \( m∠KFH = 60° \) 22. \( m∠KHL = 60° \) 23. \( m∠HKL = 60° \) 24. \( m∠KLH = 60° \)

Question 6

In triangle JHM based on congruent sides: 25. \( m∠HJM = 60° \) 26. \( m∠HMJ = 60° \) 27. \( m∠JHM = 60° \) 28. \( m∠OFK = 60° \) 29. \( m∠OKF = 60° \) 30. \( m∠KOF = 60° \)

Question 7

In triangle HKN with \( ∠HKN \cong ∠HNK \): 31. \( m∠HKN = 60° \) 32. \( m∠HNK = 60° \) 33. \( m∠OKN = 60° \) 34. \( m∠JNO = 60° \) 35. \( m∠JON = 60° \) 36. \( m∠NJO = 60° \)

With all the mentioned angles deduced based on the properties of the triangles involved, you should be able to conclude that in this triangular arrangement, the angles maintain a structured equality completing the congruent properties. So each angle measures up to 60 degrees based on the congruences stated.