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The image shows a geometry problem involving a circle, two intersecting chords, and angles. Here's a breakdown of the problem and solution provided in the image:

### Problem:
- A circle is shown with an angle of \( 40^\circ \) at the top, an angle of \( 100^\circ \) at the bottom, and two unknown angles \( x \) and \( y \).
- The goal is to find the values of \( x \) and \( y \).

### Solution Steps:

1. **Finding \( x \):**
   The angle \( x \) is formed by the intersection of two chords. In this case, \( x \) is the average of the arcs it intercepts. These arcs are \( 40^\circ \) (above) and \( 100^\circ \) (below). The formula for finding the angle formed by two intersecting chords is:
   \[
   x = \frac{1}{2} ( \text{arc1} + \text{arc2} )
   \]
   Substituting the given values:
   \[
   x = \frac{1}{2} (40^\circ + 100^\circ) = \frac

Consider the diagram below. Find the values of x and y.

Explore how to solve a geometry problem involving angles formed by intersecting chords in a circle. Using the intersecting chords theorem, this problem demonstrates key formulas for finding unknown angles x and y. Perfect for students in Grades 9-12.

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