This is the 9459th most frequent Russian word.
угадай
"Guess."
The word 'угадай' here is used as a command prompting another to try and predict my age based on their intuition or deduction.
Угадай, сколько мне лет!
Guess how old I am!
The verb 'угадываю,' derived from 'угадай,' is used here to represent the act of making a guess or assumption about the future weather.
Я угадываю, что завтра будет хорошая погода.
I guess that tomorrow the weather will be nice.
In this case, 'угадывает' means 'he guesses' and refers to his habitual action of determining who is calling based on evidence or intuition.