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The problem you've provided involves a circle with points \( A, B, C, D, E \) lying on the circle, and \( AB \) extended to \( F \). We are tasked with finding the values of \( w \), \( x \), and \( y \), given that \( \angle AED = 140^\circ \) and \( \angle CBF = 95^\circ \).

### Step-by-step solution:

#### 1. **Find \( w \):**
   - We know \( \angle CBF = 95^\circ \).
   - \( \angle CBF \) is an exterior angle of the cyclic quadrilateral \( ABCD \), and the exterior angle is equal to the opposite interior angle. Hence, \( \angle CBF = \angle CAD \).
   - Therefore, \( w = 95^\circ \).

#### 2. **Find \( x \):**
   - The opposite angles of a cyclic quadrilateral sum to \( 180^\circ \). Therefore, \( \angle AED + \angle ACD = 180^\circ \).
   - Since \( \angle AED = 140^\circ \), we can find \( x \) as follows:
   \[
   140^\circ + x = 180^\circ
   \]
   \[
   x = 180^\circ - 140^\circ = 40^\circ
   \]

#### 3. **Find \( y \):**
   - \( \angle AEB \) subtends the same arc as \( \angle ACB \) (they are angles in the same segment of the circle). Therefore, \( y = \angle ACB \).
   - From the previous calculation, we know that \( \angle ACB = x = 40^\circ \).
   - Hence, \( y = 40^\circ \).

### Final Answers:
- \( w = 95^\circ \)
- \( x = 40^\circ \)
- \( y = 40^\circ \)

Would you like any further clarifications or details on any step?

Here are 5 related questions for practice:
1. What is the sum of the opposite angles in a cyclic quadrilateral?
2. How do you find the exterior angle of a cyclic quadrilateral?
3. If the angle subtended by a chord at the center is known, how do you find the angle subtended by the same chord at the circumference?
4. What is the relationship between an exterior angle and an interior opposite angle in a cyclic quadrilateral?
5. How do you use the angles in the same segment property of a circle?

**Tip:** Always remember that in cyclic quadrilaterals, opposite angles add up to \( 180^\circ \).

A, B, C, D and E lie on the circle. AB is extended to F. Angle AED = 140° and angle CBF = 95°. Find the values of w, x, and y.

Find the values of angles w, x, and y in a circle geometry problem involving a cyclic quadrilateral. Use key theorems like the exterior angle theorem and the sum of opposite angles in cyclic quadrilaterals. Ideal for students in Grades 9-11.

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