The sum of the vertical angles is 186 degrees. find an adjacent one with a smaller angle.

Given:
lines MC and DE meet at point O,
angle MOE and angle DOC – vertical angles,
MOE angle + DOC angle = 186 degrees,
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 = 186: 2;
angle MOE = angle DOC = 93 degrees;
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 – 93;
angle MOD = 87 degrees.
Answer: 87 degrees.