The most common and most likely answer to this crossword clue is the 7 letter word RADIANS
I've seen this crossword clue in Financial Times
R
A
D
I
A
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Buddy explains!

The straight part
We know that "angular measurements" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case angular measurements = radians.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RADIANS mean?
RADIANS noun- In the International System of Units, the derived unit of plane angular measure of angle equal to the angle subtended at the centre of a circle by an arc of its circumference equal in length to the radius of the circle. Symbol: rad