Question

Prove sum of interior angle triangle is 180​

Answer 1

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 ,

• 
  `\angle` BAC +
  `\angle` BCA =
  `\angle` CBK

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

Also ,

• 
  `\angle` ABC +
  `\angle` CBK = 180°

( linear pair )

Hence from above two ,

• 
  `\angle`ABC +
  `\angle` BAC +
  `\angle` ACB = 180°

Hence Proved !