For (1), in geometry, when angles are vertically opposite, they are said to be equal. If one angle is 2x and the vertically opposite angle is x + 30, then we can equate them.
For (2), we will need to consider where each angle is located in relation to each other.
Vertically opposite angles are equal.
Two angles that make up a right angle are complementary. (two angles that add up to 90)
Angles in the same segment of a straight line with another line cutting the straight line are supplementary (such as angles COD and AOD) These two angles add up to 180
For (3), see above