**Lines and Angles Exercise 3.2**

In Exercise 3.2 of the Lines and Angles chapter, we will explore different concepts related to lines and angles. Let's go through each question and explain the solutions in detail.

**Question 1:**
In the given figure, if AB || CD, find the value of x.

Here, we are given a figure where line AB is parallel to line CD. We need to determine the value of angle x.

To solve this question, we can observe that when a transversal intersects two parallel lines, alternate interior angles are congruent. Therefore, angle x is equal to the alternate interior angle formed with line AB.

**Solution:**
Angle x = angle BCD (alternate interior angles)
Therefore, angle x = 75°

**Question 2:**
In the given figure, if AB || CD, find the value of y.

Similar to the previous question, we are given a figure where line AB is parallel to line CD. This time, we need to find the value of angle y.

Using the same concept as before, we know that when a transversal intersects two parallel lines, corresponding angles are congruent. Therefore, angle y is equal to the corresponding angle formed with line AB.

**Solution:**
Angle y = angle ACD (corresponding angles)
Therefore, angle y = 60°

**Question 3:**
In the given figure, if AB || CD, find the values of x and y.

In this question, we are given a figure where line AB is parallel to line CD. We need to determine the values of angles x and y.

By applying the concepts of alternate interior angles and corresponding angles, we can solve this question.

**Solution:**
Angle x = angle BCD (alternate interior angles)
Therefore, angle x = 80°

Angle y = angle ACD (corresponding angles)
Therefore, angle y = 60°

To summarize:
- Angle x = 80°
- Angle y = 60°

In this exercise, we have used the concepts of alternate interior angles and corresponding angles to solve the given problems. By understanding the properties of parallel lines and transversals, we can find the measures of angles accurately.