Explanation:

To find reflex angle AOD, we need to first find the measure of acute angle AOB.

Step 1: Find the measure of angle AOC

Since AOB is a straight line, we can find the measure of angle AOC by subtracting the measure of angle BOC from 180 degrees.

Angle BOC = 40 + 80 = 120 degrees

Therefore, angle AOC = 180 - 120 = 60 degrees.

Step 2: Find the measure of angle AOD

To find the measure of angle AOD, we need to add the measure of angle AOC and angle COD.

We know that angle AOC = 60 degrees.

To find the measure of angle COD, we can use the fact that angle BOC and angle COE are supplementary, meaning that they add up to 180 degrees. Therefore, angle COE = 180 - 80 = 100 degrees.

Since angle COD is an exterior angle of triangle COE, it is equal to the sum of the two remote interior angles, which are angles COE and CEO.

Therefore, angle COD = angle COE + angle CEO = 100 + 40 = 140 degrees.

Therefore, the measure of angle AOD is:

angle AOD = angle AOC + angle COD = 60 + 140 = 200 degrees.

Step 3: Find the measure of reflex angle AOD

Since angle AOD is greater than 180 degrees, it is a reflex angle.

To find the measure of the reflex angle AOD, we need to subtract the measure of angle AOB from 360 degrees.

We know that angle AOB = 180 - angle COE = 180 - 100 = 80 degrees.

Therefore, the measure of reflex angle AOD is:

reflex angle AOD = 360 - angle AOB = 360 - 80 = 280 degrees.

Conclusion:

Therefore, the reflex angle AOD is 280 degrees.

In the adjoining figure, AOB is a straight line. Find reflex angle AOD