Angle AOB is equal to 138 degrees through points A, B straight lines are drawn which are parallel to the sides of this angle

Angle AOB is equal to 138 degrees through points A, B straight lines are drawn which are parallel to the sides of this angle and intersect at point C. find the corners that formed when these lines intersect.

Since, by condition, the AC is parallel to the OB, and the BC is parallel to the OA, then OACB is a parallelogram.

In a parallelogram, opposite angles are equal, then the angle ACB = AOB = 137.

Angle DCE = ACB = 137 as vertical angles at the intersection of straight lines AE and BD.

The angle ACD is adjacent to the angle ACB, the sum of which is 180, then the angle ACD = (180 – 137) = 43.

Answer: The angles at the intersection of straight lines are 137 and 43.