The sum of the vertical angles AOB and COD, formed at the intersection of lines AD and BC, is 108 °. Find the corner BOD.

Given:
lines AD and BC intersect at point O,
vertical angles AOB and COD,
angle AOB + angle COD = 108.
Find the degree measure of the angle BOD -?
Decision:
We know that the vertical angles are equal to each other. Then angle AOB = angle COD. Since the angle AOB + angle COD = 108, then
angle AOB = angle COD = 108: 2;
angle AOB = angle COD = 54 degrees.
Angle AOB and angle BOD are adjacent. The sum of adjacent angles is 180 degrees, then
angle BOD = 180 – angle AOB,
angle BOD = 180 – 54;
BOD angle = 126 degrees.
Answer: 126 degrees.