Lines AB, CD and EF intersect at point O. Moreover, AB is angle CD. Angle AOE = 30 degrees.

Lines AB, CD and EF intersect at point O. Moreover, AB is angle CD. Angle AOE = 30 degrees. Find the COF angle measure.

Let’s analyze the conditions of the task:

AB is perpendicular to CD, as specified.
O is the intersection point of lines AB, CD, EF.
∠AOE = 30 °.
∠COF = to be found.
We will place AB horizontally, this line will be an unfolded angle and will be equal to 180 °.
Knowing that AB is perpendicular to CD, the angles will be right, i.e. 90 ° each (these are the angles AOD, BOD, AOC, BOC).
However, the straight lines located at the extended corner acquire the property of adjacent corners.
Hence, ∠COF = AB – ∠AOE – ∠BOC = 180 ° – 30 ° – 90 ° = 60 °.
Answer: ∠COF = 60 °.