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

1) What is the degree measure of the angle MOE?

Since at the intersection of straight lines MC and DE two pairs of vertical angles are formed, and, as you know, the vertical angles are equal, then the angle MOE = angle DOC = 204˚: 2 = 102˚.

2) What is the angle MOD?

Angle MOD = 180˚ – angle MOE = 180˚ – 102˚ = 78˚.

Answer: The degree measure of the angle MOD is 78˚.