Respuesta :

VirαtKσhli

Given :-

  • A triangle ABC .

To prove :-

  • Sum of interior angles of a ∆ is 180° .

Construction :-

  • Draw a line MCN parallel to AB .
  • Extend line AB to K .

Proof :-

In ∆ ABC , we have ,

  • [tex]\angle[/tex] BAC + [tex]\angle[/tex] BCA = [tex]\angle[/tex] CBK

As sum of two interior angles of a triangle is equal to the opposite exterior angle .

Also ,

  • [tex]\angle[/tex] ABC + [tex]\angle[/tex] CBK = 180°

( linear pair )

Hence from above two ,

  • [tex]\angle[/tex]ABC + [tex]\angle[/tex] BAC + [tex]\angle[/tex] ACB = 180°

Hence Proved !

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