Is the word their a vowel pair or a vowel r word?

Question

This if for a syllable sorting exercise.

Answer 1

There are four types of r-controlled words (r-words)

'schwa+r' /ɚ/

'ar sound' /ɑr/

'or sound' /ɔr/

'air sound' /ɛr/

When we transcribe 'their' in phonetic symbols, it is written as

ðɛr

Although by definition it can be confused as a vowel pair word because there is a pair of vowels in the word that stands for one phoneme, the length and nature of the vowel /ɛ/ is controlled by the ending /r/. So, it is an r-controlled word.