1. The photo was taken from an unusual angle.

2. The photo was taken at an unusual angle.
(Which preposition do we have to use? Are both OK?)

3. Bend your knees and bend your body at 45 degree angle.

4. Bend your knees and bend your body from 45 degree angle.
(Which preposition do we have to use? Are both OK?) •English - Writeacher, Monday, April 4, 2016 at 6:46am
1 and 2 -- both are OK.

3 and 4 -- both need "... a 45-degree angle."
The prepositions are OK.

..........
Scroll down a bit and read Hyphens have other uses section. The hyphen I used above fits the "a" use.
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1-1. The photo was taken from an unusual angle.

1-2. He took the photo from an unusual angle.

1-3. He took the photo at an unusual angle.
(Are they all grammatical? Don't we have to use 'at' before 'angle'?)

No, you do not need "at" before "angle". You already have used a preposition, "from" and "at" in the sentences. "at an angle" is the prepositional phrase, with the adjective "unusual". The same for the other two sentences.

All three sentences are correct as you have written them.

All three sentences are grammatically correct.

In sentence 1-1, "from" is used to indicate the source or starting point of the action. When we say "taken from an angle," it means that the photo was captured from a particular perspective.

In sentence 1-2, "from" is also used to indicate the starting point or source, but here it is referring to the photographer who took the photo. So, we can say "He took the photo from an unusual angle" to show that he captured the photo from a unique perspective.

In sentence 1-3, "at" is used to indicate a specific location or point in space. So, "He took the photo at an unusual angle" implies that the photo was captured from a distinctive position or viewpoint.