"... what kind of everyday situations annoy/annoys them."

[Mori]

Here's the complete sentence:

"Have Ss tell the class what kind of everyday situations annoy them.|

Source: Jack C. Richards & Chuck Sandy, Passages 1 third edition, Teacher's edition, page T-80

I think kind is the head of the noun phrase, so the verb should be annoys. Please correct me if I'm wrong.

 

[Amigos4]

The correct sentence is: "What kind of everyday situations annoy them?"

In this sentence, the verb must agree with the subject, which is "situations," not "kind." The verb is "annoy".
"What kind of" acts as a determiner or a modifying phrase for the subject.

 

[Mori]

The correct sentence is: "What kind of everyday situations annoy them?"

In this sentence, the verb must agree with the subject, which is "situations," not "kind." The verb is "annoy".
"What kind of" acts as a determiner or a modifying phrase for the subject.

Thanks for the answer, but isn't it similar to the following sentence?
A large basket of apples is sitting on the kitchen table.

 

[jutfrank]

... isn't it similar to the following sentence?
A large basket of apples is sitting on the kitchen table.

Not where it counts. There, basket is the head and subject of the NP, and so controls agreement.

what kind/sort of + plural NP phrases are different in that agreement comes from the plural noun, not from the singular sort/kind that appears at first sight to be the head.

 

[Piscean]

I agree with Mori on this

Michael Swan (2016, section 593) says that both singular and plural forms are possible the latter being less formal.

 

[Annabel Lee]

"Have Ss tell the class what kind of everyday situations annoy them.|

. . . I think kind is the head of the noun phrase, so the verb should be annoys.

I find the singular a bit awkward there, but only because I'd more naturally use "what kinds" (plural) here rather than "what kind":

Have students tell the class what kinds of situations annoy them.​

​

Most people are capable of being annoyed by various kinds of situations (being locked out of the house, being stung by a bee, being scolded by one's boss, and so forth), so why should the question be limited to just one kind of situation?

Regarding the grammar of it, the choice for me would be singular in the following, though I can easily imagine people using the plural in less formal English. I might even find myself doing so in grammatically unguarded, live conversation.

Have each student tell the class what kind of apples he thinks is the best.​

What kind of apples is the best?​

 

[emsr2d2]

Have each student tell the class what kind of apples he thinks is the best.​

For the benefit of learners here, it's worth noting that the sentence above (in the UK in this day and age, at least) would be used only if the class consisted entirely of boys/men. For a mixed-gender class, we'd use "... what kind of apples they think is the best".