Pique (pēk)

The verb pique means to make someone angry or annoyed. But when something piques your interest or curiosity, here the verb pique just means to arouse, stimulate, or excite, Also, it can be used as a word to denote the feeling of being offended or resentful after a slight or indignity. Also, it is tightly woven fabric with raised cords

In short, one shall derive the meaning of pique based on the occasion / particular sentence.

This is borrowed from a French word meaning a prick or irritation from Old French piquer, “to prick” So you can see how something that piques you could make you both excited and angry, perhaps even enough to storm away.

Example
In a pique, I foolishly declined the invitation to attend the concert. (meaning as feeling of annoyance)

He stormed from the room in a fit of pique, shouting that he had been misunderstood (meaning as feeling of annoyance)

Five years later, he created the original cotton pique shirt embroidered with the famous crocodile. (meaning as fabric)

What we want to do first, though, is to pique your interest by sharing some of the accomplishments. (meaning as arouse / excite)