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The image you provided shows a circle with an inscribed quadrilateral, where two angles are given: 40° and 43°. Let's break this down:

1. The quadrilateral is cyclic, meaning all its vertices lie on the circumference of the circle.
2. In a cyclic quadrilateral, opposite angles are supplementary, meaning they sum to 180°.

The given angles are:
- One angle is 40°
- Another angle is 43°
- The angles \( x \) and \( y \) are unknown.

Now, let's solve for \( x \) and \( y \):

- \( 40^\circ \) and \( x \) are opposite angles. Therefore, \( 40^\circ + x = 180^\circ \), which gives \( x = 180^\circ - 40^\circ = 140^\circ \).
- \( 43^\circ \) and \( y \) are opposite angles. Therefore, \( 43^\circ + y = 180^\circ \), which gives \( y = 180^\circ - 43^\circ = 137^\circ \).

Thus:
- \( x = 140^\circ \)
- \( y = 137^\circ \)

Would you like more details or clarifications on any step?

### Related Questions:
1. What are the properties of a cyclic quadrilateral?
2. Can you explain why opposite angles in a cyclic quadrilateral are supplementary?
3. What other types of figures can be inscribed in circles?
4. How do the internal angles of a cyclic quadrilateral relate to its exterior angles?
5. What happens if a quadrilateral is not cyclic, but still drawn inside a circle?

### Tip:
In geometry, recognizing that a quadrilateral is cyclic (inscribed in a circle) can simplify solving problems using angle relationships.

Solve for the angles x and y in a cyclic quadrilateral where two angles are 40° and 43°.

Learn how to solve for unknown angles in a cyclic quadrilateral where two angles are 40° and 43°. This solution involves the theorem that opposite angles in a cyclic quadrilateral are supplementary, a key concept in geometry. Suitable for students in Grades 9-10.

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