Cryptic crossword clue
Chap to study fragments of tile with instrument for measuring angles

The most common and most likely answer to this crossword clue is the 10 letter word THEODOLITE

I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "instrument for measuring angles" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case instrument for measuring angles = theodolite.
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 THEODOLITE mean?

THEODOLITE noun
  1. A surveying instrument, consisting of a small mounted telescope, used to measure horizontal and vertical angles.

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