Straight lines AD and BC intersect at point O. inside the angle AOB, point M is taken, and inside the angle

Straight lines AD and BC intersect at point O. inside the angle AOB, point M is taken, and inside the angle COD, point K. AOB = 80, MOB = 30. KOD = 40 a) Find the angles AOM and COK. b) Are the angles MOB and COK vertical?

Vertical angles are formed when two straight lines intersect and are pairs of angles with a common vertex that are equal to each other.

A) AOM = AOB – MOB = 80º – 30º = 50º.
The angles CОD and AOB are vertical, which means they are equal, CОD = AOB = 80º.
Angle COK = COD – KOD = 80º – 40º = 40º.
B) For the angles MOB and CОK to be vertical, it is necessary that they be equal.
But from the previous assignment we found out that this is not so, COK = 40º, MOB = 30º.
Therefore, the angles MOB and COK are not vertical.