The sum of the vertical angles is 108 degrees to find the remaining angles.

1. ∠АОВ and ∠СОВ, ∠АОС and ∠ ВОД – vertical angles. ∠АВ + ∠СОВ = 108 °.

1. Considering that the vertical angles are equal (according to their properties), and their sum is equal to 100 ° according to the problem statement, we calculate their value:

∠АВ = ∠СОВ = 108 °: 2 = 54 °.

2. Taking into account that ∠ЕОМ and АОС are adjacent angles, and their total value is 180 °, we calculate the degree measure AOC:

АС = 180 ° – ∠АВ = 180 ° – 54 ° = 126 °.

3. ∠AOC = ∠BOD. ∠BOD is also 126 °.

Answer: ∠АОВ = ∠СОВ = 54 °, ∠AOC = ∠СОD = 126 °.