Python 2, 55 54 51 57 bytes

^{-3 bytes (and a bug fix) thanks to Felipe Nardi Batista}

i=0
for c in input():i-=i and c<'<';print' '*i+c;i+=c>'<'

Try it online!

Python 2, 55 54 51 57 53 bytes

^{-3 bytes (and a bug fix) thanks to Felipe Nardi Batista}

i=0
for c in input():i-=c<'<'*i;print' '*i+c;i+=c>'<'

Try it online!

Python 2, 55 54 51 bytes

^{-3 bytes thanks to Felipe Nardi Batista}

i=1
for c in input():i-=c<'<';print' '*i+c;i+=c>'<'

Try it online!

The extra space is allowed in the rules

Each line may have extra trailing whitespace as long as this doesn't change the visual appearance of the output.

Python 2, 55 54 51 57 bytes

^{-3 bytes (and a bug fix) thanks to Felipe Nardi Batista}

i=0
for c in input():i-=i and c<'<';print' '*i+c;i+=c>'<'

Try it online!

Python 2, 55 54 51 bytes

^{-3 bytes thanks to Felipe Nardi Batista}

i=1
for c in input():i-=c<'<';print' '*i+c;i+=c>'<'

Try it online!

Python 2, 55 54 51 bytes

^{-3 bytes thanks to Felipe Nardi Batista}

i=1
for c in input():i-=c<'<';print' '*i+c;i+=c>'<'

Try it online!

The extra space is allowed in the rules

Each line may have extra trailing whitespace as long as this doesn't change the visual appearance of the output.