Here are the correct forms of the words given for each sentence:

29. We should think about how English **widens** our knowledge when we surf the internet. (wide)

30. Those archeological discoveries are enormously **valuable** to historians. (value)

31. The boy blushed with **embarrassment** when he heard his mom call his nickname in public. (embarrass)

32. My hometown has changed a lot, but **thankfully** the skatepark I like still remains. (thank)

33. According to him, he likes a job that doesn’t involve **communicating** with many people. (communicate)

34. The hotel has several **vacancies** available for the upcoming holiday weekend. (vacant)

Feel free to ask if you need further assistance!