Step 1: Conceptual Understanding:
The query requires identification of the individual who posed the seminal question to sage Aṅgiras within the Mundaka Upaniṣad, initiating the text's philosophical exploration.
Step 2: Detailed Explanation:
The Mundaka Upaniṣad commences by outlining its knowledge transmission lineage. It then records that a distinguished householder (mahāśāla) named Śaunaka approached sage Aṅgiras and posed the critical inquiry: "kasmin nu bhagavo vijñāte sarvamidaṃ vijñātaṃ bhavatīti," which translates to "Revered sir, what is that by knowing which all this becomes known?".
This question prompts Aṅgiras to elucidate the two categories of knowledge: the lower (Aparā Vidyā – encompassing the Vedas, grammar, etc.) and the higher (Parā Vidyā – the comprehension of the immutable Brahman).
The other figures mentioned are notable individuals from different Upanishads:
Uddālaka and his son Śvetaketu are prominent in the Chāndogya Upaniṣad, recognized for the "Tat Tvam Asi" discourse.
Janaka, the king of Videha, is a significant philosopher-king featured in the Bṛhadāraṇyaka Upaniṣad.
Step 3: Conclusion:
Śaunaka was the individual who approached Aṅgiras with this pivotal question in the Mundaka Upaniṣad. Consequently, option (2) is the correct answer.