The difference between the degree measures of two adjacent angles is 122 degrees.

The difference between the degree measures of two adjacent angles is 122 degrees. Find the degree measure for each of these angles.

Let MOC and KOR be adjacent angles (angle MOP is a deployed angle).

By condition, their difference is equal to 122 °:

MOК – KOR = 122 °.

Let MOК be equal to x, then the angle KOР will be equal to (180 ° – x), since the sum of adjacent angles is 180 °.

x – (180 – x) = 122.

x – 180 + x = 122.

2x = 122 + 180.

2x = 302.

x = 151 ° (angle MOK).

Then the angle KOР = 180 ° – 151 ° = 29 °.

Answer: The angles are 29 ° and 151 °.