The sum of the vertical angles MOE and DOC, formed at the intersection of lines MC and DE

The sum of the vertical angles MOE and DOC, formed at the intersection of lines MC and DE, is 204 (degrees). Find the corner MOD.

Given:
lines MC and DE meet at point O,
angle MOE and angle DOC – vertical angles,
angle MOE + angle DOC = 204,
Find the degree measure of the angle MOD -?
Decision:
1) Consider the vertical angles MOE and DOC. We know that the vertical angles are equal to each other. Then
angle MOE = angle DOC;
angle MOE = angle DOC = 204: 2;
angle MOE = angle DOC = 102;
2) Angle MOD and angle MOE are adjacent. We know that the sum of the degree measures of adjacent angles is 180 degrees.
angle MOD = 180 – 102;
angle MOD = 78 degrees.
Answer: 78 degrees.