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To solve this problem, we can apply the **Triangle Angle Sum Theorem**, which states that the sum of the interior angles of a triangle is always 180°.

The triangle has the following angles:

1. One given angle of 114°.
2. Two angles labeled as \( y \) and \( y' \), which seem to be equal, suggesting this is an isosceles triangle.

### Step-by-step solution:

1. Let both \( y \) and \( y' \) represent the two unknown angles.
2. The sum of the three angles of a triangle is 180°. Therefore, we can write the equation:
   \[
   114^\circ + y + y = 180^\circ
   \]
   Simplifying the equation:
   \[
   114^\circ + 2y = 180^\circ
   \]
3. Subtract 114° from both sides:
   \[
   2y = 180^\circ - 114^\circ = 66^\circ
   \]
4. Divide both sides by 2 to find \( y \):
   \[
   y = \frac{66^\circ}{2} = 33^\circ
   \]

Thus, the value of \( y \) is **33°**, which corresponds to option **C**.

Would you like any further details or have any questions?

### Related Questions:
1. How can we prove that the sum of angles in a triangle is always 180°?
2. What are the properties of an isosceles triangle?
3. How would the solution change if the triangle were not isosceles?
4. Can this method be used to solve for angles in non-Euclidean geometry?
5. What are the applications of the Triangle Angle Sum Theorem in real-world problems?

### Tip:
Always remember to check whether the triangle given is isosceles, scalene, or equilateral. This helps in simplifying the problem-solving process.

What is the value of y in the given triangle with one angle of 114° and two equal angles labeled as y?

In this geometry problem, find the value of the unknown angle y in an isosceles triangle with one angle of 114°. The solution uses the Triangle Angle Sum Theorem. Suitable for students in Grades 7-9.

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