The Sun Temple of Konark was indeed built by Narasimhadeva I. To understand which dynasty he belonged to, let`s dissect each option:

Option 1: Somavamsi dynasty - This dynasty existed from the 9th to the 12th century and ruled parts of eastern India. However, Narasimhadeva I was not a part of this dynasty.

Option 2: Imperial Ganga dynasty - This is the correct answer. The Imperial Ganga dynasty ruled the Kalinga region (modern-day Odisha) from the 11th to the 15th century. Narasimhadeva I belonged to this dynasty and was responsible for the construction of the Sun Temple of Konark.

Option 3: Suryavamsi Gajapti dynasty - This dynasty was a medieval Hindu dynasty that ruled over parts of present-day Odisha and Andhra Pradesh. However, Narasimhadeva I was not a part of this dynasty.

Option 4: Bhoi dynasty - The Bhoi dynasty is not historically known to have ruled over the region during the time of the Sun Temple`s construction. Therefore, Narasimhadeva I did not belong to this dynasty.

In conclusion, the