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.

Question

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 =

Answer 1

To find the angle measures for the given triangles and properties of the swan, we'll use the information provided along with some basic properties of triangles and isosceles triangles.

Given Information:

1. ΔABC is equilateral, meaning:

   • m∠ABC = m∠BCA = m∠CAB
   • Since it is equilateral, each angle measures 60 degrees.

2. DE ≅ CE ≅ EF:

   • Triangles involving these segments will be isosceles.

3. KO ≅ FO:

   • Triangles involving these segments will also be isosceles.

4. JN ≅ JO:

   • Similar to the above, these segments create isosceles triangles.

5. ∠BCD ≅ ∠BDC:

   • This indicates that triangle BCD is isosceles with the equal angles being ∠BCD and ∠BDC.

6. CGF ≅ ∠CFG:

   • Another isosceles triangle with base angles that are equal.

7. ∠HKN ≅ ∠HNK:

   • Yet another isosceles triangle.

8. ΔGCF ≅ ΔGKF ≅ ΔJHM:

   • These triangles are congruent to each other.

9. ΔKFH ≅ ΔKLH:

   • These triangles are also congruent to each other.

Calculation of Angles:

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

Since triangle ABC is equilateral, all angles are 60 degrees.

Next, we'll calculate the angles in triangle BCD, which is isosceles, since ∠BCD ≅ ∠BDC.

Let m∠BCD = x and m∠BDC = x. The third angle, ∠CBD, can be found using the triangle sum theorem (180 degrees):

• \( m∠BCD + m∠BDC + m∠CBD = 180° \)
• \( x + x + m∠CBD = 180° \)
• \( 2x + m∠CBD = 180° \)

We also know that since ∠BCD ≅ ∠BDC, the angles must also add up to 180°. Thus:

4. To determine x:

   • Since we don't have specific angles from the diagram, we can assume a common measure for the angles.
   • Let's assume x = 70° (as an example), then:
   • \( 2(70°) + m∠CBD = 180° \)
   • \( 140° + m∠CBD = 180° \)
   • \( m∠CBD = 40° \)

5. m∠BCD = 70°

6. m∠BDC = 70°

7. m∠CBD = 40°

Final Angles:

1. m∠ABC = 60°
2. m∠BCA = 60°
3. m∠CAB = 60°
4. m∠BCD = 70° (hypothetical)
5. m∠BDC = 70° (hypothetical)
6. m∠CBD = 40° (hypothetical)

Please adjust the second set of angles based on the actual figure or any additional context provided in your drawings or descriptions.