# internal angle sum of triangle

#### halo1234

Problem: Let A, B, C be three non-collinear points. Let D, E, F be points on the respective interiors of segments BC, AC and AB. Let ?, ? and ? be the measures of the respective angles ?BFC, ?CDA and ?AEB. Prove IAS(ABC) < ? +? + ? < 540 - IAS(ABC).(IAS means internal angle sum). Now I'm supposed to use the external angle inequality which is the measure of an exterior angle of a triangle is greater than that of either opposite interior angle. Not sure how to do it. I've been struggling for hours with it. Oh I forgot to mention this is still in absolute geometry so we can't use that the angles of a triangle add up to 180°.

#### anonimnystefy

If I remember correctly, the internal angle sum of a triangle is derivable from the axioms of absolute geometry (as long as you have a concept of an angle).