Why is the king relieved when he finds out that Psyche is the "Accursed"?

The King of Glome is relieved to discover that Psyche is the "Accursed," because he will not then have to die as a sacrifice to placate the Shadowbrute, the so-called god of the Mountain.
In Chapter Five, we learn that Glome has been plagued with famine, drought, and sickness. Other kings, sensing the weakness of the king of Glome, capitalize on Glome's suffering to threaten wars and rebellions. Meanwhile, the priest of Ungit tells the king that a sacrifice must be made to appease the Brute before it is too late. He maintains that the sacrifice must be "perfect" to be accepted as the Great Offering. As a warning, the priest cautions that the king must not shirk his duty, or the people of Glome will burn him alive in his palace.
By now, the king of Glome is beginning to fear that he is to be the Great Offering for the Shadowbrute. Trying to buy time, the king claims never to have heard of the Brute in his time; he tells the priest of Ungit that the Shadowbrute is a tale of his grandmother's. The priest is not to be deterred, however.
He relates that the people have already cast "holy lots" to discover the identity of the "Accursed." In the end, it has been determined that the "Accursed" resides in the king's house. Upon hearing this, the king is stricken with terror (he thinks that the priest is about to announce that he, the king, is to be the sacrifice). So, he calls on his palace guards to kill the temple guards that are gathered at the vicinity of his palace. However, his guards refuse to fight for him. The priest accuses the king of foolishness, telling him that the population is armed and ready to do violence if the king does not capitulate to their will.
Felling cornered, the king pulls out his dagger and threatens to kill the priest. However, the priest manages to repel the king by promising that he will haunt him even after his death. Defeated, the king demands to know who the "Accursed" really is. The priest eventually answers that it is the Princess Istra (or Psyche), the king's third daughter.
Upon hearing this, the king is visibly relieved that he is not to be sacrificed for the good of Glome. He then pretends to be sad that Psyche is to be the sacrifice. Meanwhile, Orual, distressed that her sister is to be the Great Offering and horrified that her father does not mean to save Psyche, tries to beg for Psyche's life. For his part, the king violently flings Orual away, as she falls at his feet in supplication. Distressed beyond endurance at the turn of events, Orual faints; she is revived in the next chapter.