Because they are alternate interior angles.
because they are corresponding angles.
because they are alternate exterior angles.
because they are same-side interior angles.

Because they are corresponding. That means that they sit in the exact same place within their own group of angles. That means, however, that lines a and b have to parallel. It's not marked that they are, but I'm assuming they must be by the answer choices you provided.

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since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.