In which of the following sentences do the subject and verb agree? susan said that measles are the worst disease that she's ever had. civics are the hardest subject that i am taking this year. john said that mathematics is his favorite subject. today's news are all bad.

I think the answer would be: John said that mathematics is his favorite subject.

The subject John agrees with the verb is. In this case said can go with the word is. After reading this sentence it seems as if he is currently taking the course and that is why the present tense is, is being used.

Hopefully this helped and good luck.

Extra:

The sentence dealing with Susan: Susan said that measles are the worst disease that she's ever had. said and are I don't think agree with each other. If the sentence went like: Susan said that measles were the worst disease that she'd ever had. I put the verbs  in past tense, making the verbs agree with the word said, which is past tense of say.  Also one can assume that she has had the measles and but currently doesn't.

If you reword the Civics sentence to: Civics classes are the hardest subjects I'm taking this year. When reading this reworded sentence everything makes more sense than the original.  

c. explains words’ origins and variations.

the knight would die while giong on a quest.