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If in an octahedral structure there is one lone pair placed on any two of the axial position then will the lone pair distort all the 90 degree angles due to repulsion from lone pair or the angles will remain same? I found one question regarding $\ce{BrF5}$.

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You are right! You asked the question and you replied simultaneously. According to this website, the structure of bromine pentafluoride confirmed your claims.

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