Two pipes merge into one pipe, through a symmetrical Y-shaped connector. If the small angle of the Y-shaped connector is 21 degrees, how many degrees is one of the large angles?

*Give your answer to 2 decimal place accuracy.*

Given that the Y-shaped connector is symmetrical, the small angle is located where the two pipes merge, and the two large angles are equal. 

### Steps to Solve:
1. **Sum of Angles in a Triangle**: In any triangle, the sum of the interior angles is \(180^\circ\).
   
2. **Determine the Two Large Angles**: Since the connector is symmetrical, the two large angles are equal. Let's denote each of these large angles as \(x\).

3. **Equation Setup**: The sum of the small angle and the two large angles must equal \(180^\circ\).
   \[
   21^\circ + 2x = 180^\circ
   \]

4. **Solve for \(x\)**:
   \[
   2x = 180^\circ - 21^\circ = 159^\circ
   \]
   \[
   x = \frac{159^\circ}{2} = 79.5^\circ
   \]

### Final Answer:
Each of the large angles is \(79.50^\circ\). 

Would you like more details or have any other questions?

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1. How do you calculate the sum of angles in different polygons?
2. How does symmetry affect angle calculations in geometric problems?
3. What is the role of supplementary angles in solving Y-shaped connector problems?
4. How can trigonometric functions be applied to problems involving angles in Y-connectors?
5. How would the calculation change if the small angle was different?
6. What if the Y-shaped connector was not symmetrical?
7. Can you derive the formula for the angles in a symmetrical Y-shaped connector?
8. How are these principles applied in real-life engineering designs?

**Tip:** When working with symmetrical figures, symmetry often simplifies your calculations by reducing the number of variables.

Learn how to calculate the large angles in a symmetrical Y-shaped connector using geometry principles. Detailed step-by-step solution provided with a focus on triangle angles and symmetry. Suitable for high school students studying geometry.

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