Given figure:

In the given figure, we have two lines AB and CD intersecting each other at point O. We need to find the value of angle x.

Explanation:

To find the value of angle x, we will use the properties of angles formed by intersecting lines.

1. Linear Pair:
When two lines intersect, they form pairs of opposite angles. These opposite angles are called linear pairs and they are always supplementary, which means the sum of their measures is 180 degrees.

In this figure, angle AOC and angle BOD are linear pairs. So, we can write:

Angle AOC + Angle BOD = 180°

2. Corresponding Angles:
When a transversal intersects two lines, it forms pairs of corresponding angles. Corresponding angles are congruent (i.e., they have the same measure) if the two lines are parallel.

In this figure, angle AOC and angle COD are corresponding angles. Since AB and CD are not parallel, angle AOC and angle COD may have different measures.

3. Vertical Angles:
When two lines intersect, they form pairs of vertical angles. Vertical angles are congruent (i.e., they have the same measure).

In this figure, angle AOB and angle COD are vertical angles. So, we can write:

Angle AOB = Angle COD

4. Solving for angle x:
From the given figure, we can see that angle AOC is equal to x degrees.

Using the properties mentioned above, we can set up the following equations:

Angle AOC + Angle BOD = 180°
x + Angle BOD = 180°

Angle AOB = Angle COD

Since angle AOB and angle COD are vertical angles, they are congruent. Therefore, we can write:

Angle AOB = Angle COD
x = Angle COD

So, we can conclude that angle x is equal to the measure of angle COD.

Conclusion:

To find the value of angle x in the given figure, we need to determine the measure of angle COD. The measure of angle COD can be found by using the properties of angles formed by intersecting lines.

I can send you the answer but where is the figure