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 !