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Question Number 1387 by navajyoti.tamuli.tamuli@gmail. last updated on 27/Jul/15

Q. is there any angle in a circle?

$${Q}.\:{is}\:{there}\:{any}\:{angle}\:{in}\:{a}\:{circle}? \\ $$

Commented by Rasheed Soomro last updated on 28/Jul/15

Two answers can be given.Each has  its  own reasoning.  (i) There are infinity number of angles.  Consider a polygon of n angles inscribed in a circle:  n→∝⇔polygon→circle ,which means A circle has ∝ angles.  (ii) There is no angle.  If an angle is defined with its arms straight,as in common  geometry a circle has 0 angles.

$${Two}\:{answers}\:{can}\:{be}\:{given}.{Each}\:{has}\:\:{its}\:\:{own}\:{reasoning}. \\ $$$$\left({i}\right)\:{There}\:{are}\:{infinity}\:{number}\:{of}\:{angles}. \\ $$$${Consider}\:{a}\:{polygon}\:{of}\:{n}\:{angles}\:{inscribed}\:{in}\:{a}\:{circle}: \\ $$$${n}\rightarrow\propto\Leftrightarrow{polygon}\rightarrow{circle}\:,{which}\:{means}\:{A}\:{circle}\:{has}\:\propto\:{angles}. \\ $$$$\left({ii}\right)\:{There}\:{is}\:{no}\:{angle}. \\ $$$${If}\:{an}\:{angle}\:{is}\:{defined}\:{with}\:{its}\:{arms}\:\boldsymbol{\mathrm{straight}},{as}\:{in}\:{common} \\ $$$${geometry}\:{a}\:{circle}\:{has}\:\mathrm{0}\:{angles}. \\ $$

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