**Solution:**

To find the measure of angle AOD, we can use the properties of intersecting lines and angles.

Let's break down the problem into smaller steps:

**Step 1: Identifying Angle Relationships**

When two lines intersect, they form four angles at the intersection point. In this case, the lines AB and CD intersect at point O, so the four angles formed are:

1. Angle AOC
2. Angle BOC
3. Angle AOD
4. Angle BOD

We are given that angle AOC is equal to angle BOD, and its measure is 130 degrees. Let's represent this information as an equation:

Angle AOC = Angle BOD = 130 degrees

**Step 2: Relationship between Vertically Opposite Angles**

When two lines intersect, the opposite angles formed are called vertically opposite angles. These angles are equal in measure. In this case, angles AOC and BOD are vertically opposite angles.

From the given information:

Angle AOC = Angle BOD = 130 degrees

**Step 3: Relationship between Angles on a Straight Line**

When a straight line intersects two other lines, the sum of the angles on one side of the intersection point is equal to 180 degrees. In this case, angles AOC, COB, and BOD are on one side of the intersection point O.

From the above step, we know:

Angle AOC + Angle BOD = 130 degrees

And since angle COB is on the same side, we can write the equation:

Angle AOC + Angle COB + Angle BOD = 180 degrees

**Step 4: Finding Angle AOD**

We are asked to find the measure of angle AOD. Since angles AOC, COB, and BOD add up to 180 degrees, we can subtract the sum of angles AOC and COB from 180 to find the measure of angle AOD.

From the equation in the previous step:

Angle AOC + Angle COB + Angle BOD = 180 degrees

Substituting the known values:

130 degrees + Angle COB + 130 degrees = 180 degrees

Simplifying the equation:

Angle COB = 180 degrees - 130 degrees - 130 degrees
Angle COB = -80 degrees

Since angles cannot have negative measures, we made an error in our calculations or there might be a mistake in the given information. Please recheck the problem and provide the correct values or information to proceed with the solution.

given: aoc +bod = 130to find :aod procedure : we know that aod=cobso let aod=x and cob=x so x+x+aoc+dob=360 so 2x +130=360 so 2x=230so x= 115so this implies aod =115