Final answer:
Odysseus' anger over the bed being moved is significant to Penelope as it confirms his identity due to their shared secret knowledge about the bed's immobility, emblematic of their solid marriage and history together.
Step-by-step explanation:
Odysseus' anger over the bed being moved is a good sign for Penelope because it signifies that he is indeed the real Odysseus. In Homer's The Odyssey, the bed represents Odysseus and Penelope's marriage and is a symbol of their shared history and love.
Since Penelope knows that the bed was built around a living olive tree by Odysseus and could not be moved, his reaction to her pretending to move it confirms his identity and his lasting bond with her. This test of the bed is a pivotal moment for Penelope, signaling that her long-lost husband has returned and thus bringing an end to her uncertainty and fears.
Odysseus' knowledge of the immovable bed, which is unknown to others, demonstrates not only their intimate knowledge of one another but the bed also serves as testament to their relationship's resilience. This secret knowledge is something only the true Odysseus would possess, and his rage at the idea of its movement is proof of authenticity to Penelope.