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

This task does not require constructions, since it is solved with the help of several logical inferences.

When two straight lines intersect, four angles are formed, the values of which are pairwise equal. In this case, the sum of all angles will be 360 °, and the sum of two adjacent angles will be 180 °.

If the sum of two opposite angles (AOB and COD) is 108 °, then the value of one of these angles:

108о / 2 = 54о

Hence the value of the adjacent BOD angle:

180o – 54o = 126o

Verification:

54о * 2 + 126о * 2 = 360о

Answer: The BOD angle is 126o.