I came across this in my book that"The portion common to both shadings is called the interior of ∠ABC" and i also have read that "In a closed curve, there are three parts. (i) interior (‘inside’) of the curve (ii) boundary (‘on’) of the curve and (iii) exterior (‘outside’) of the curve" but, If angle is not a closed figure, then how does it contain interior points?
Thanks for replying, yea true i was reading and i get confused as
1.) why angles not being a closed curve have interior parts,
2.) what if the angle is 180 degree which part is exterior and which is interior.Considering an angle 60 degree its interior part is the area common to the sides but
3.) what about 150 degree interior part ? can we still say the same common area under to both the sides. Is this true? .
4.) One more thing does the points on the boundary of the angle(basically rays) and on the origin(0,0) are also included in interior point of that angle? My opinion is if placed on coordinate axes the horizontal ray will look like (x,0) and vertical ray(assuming 90 degree angle) (y,0) so boundary points are interior points and point on origin is exterior. i am confused Please correct me if i am wrong
The quoted passage
describes the "interior points" of a closed curve. It does not provide any guidance for things which are not closed curves. You observe that an angle is not a closed curve. Therefore, the definition above provides no guidance about interior points of an angle.
A less abstract parallel may be helpful. We are told that "time flies like an arrow." Does this provide any guidance on how fruit flies? (... with apologies to E.B. Oettinger.)
Actually, since the description of closed curves does not give guidance on interior points of an angle, you have to be told explicitly which points of an angle are interior points, which is what the image you have included is doing.