angaega kkyeoyo.

In Korean, when a verb stem ends in -이 (here 끼-) and you add -어요, the 이 disappears and 어 becomes 여. So:
끼 + 어요 → 껴요

The dictionary form is 끼다. In this sentence 끼다 means “to form” or “to settle,” as in fog or mist gathering.

-가 marks the grammatical subject, introducing new information: “Fog is gathering.”
-는 (topic marker) would imply “As for the fog…” and might contrast with something else. Both are possible, but 안개가 껴요 is the neutral way to report “It’s foggy.”

껴요 is present tense in the informal polite style (also called “Polite/Standard” speech). You’d use it with strangers, colleagues, or in public announcements. It’s neither overly formal nor casual.

Change 껴요 to the past polite form 꼈어요. Note the spelling change:
끼 + 었어요 → 꼈어요
So you get 안개가 꼈어요 (“It was foggy.”).

Yes, 안개가 있어요 literally means “There’s fog,” but 안개가 껴요 more naturally describes a weather condition: “It’s foggy” or “Fog is forming.”

Aside from “fog/mist gathering,” 끼다 can mean:
• “to wear” (e.g. 반지를 끼다 – to wear a ring)
• “to get caught/inserted” (e.g. 문에 손가락이 꼈어요 – my finger got caught in the door)
• “to cloud over” (e.g. 안경에 김이 껴요 – my glasses are fogging up)