Which of the following pair of angles are vertical angles?

To find out which pair of angles are vertical angles. We must know that:

As for angles I & II, they are not vertical angles. This is because these two angles are adjacent angles.

Similarly, angles II & III and III & IV are not vertical angles for the same reason as above.

Only angles I & III are vertical angles as these angles fulfill the properties mentioned in Step 1. Hence, the answer is D.

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