Question

show that an interior angle of a triangle is equal to the sum of two opposite inerior angles.
Please tell the answer from class 7th NCERT ​

Answer 1

Given :  Correct question Exterior angle of triangle is equal to sum of two opposite interior angles  

To Find :  Prove

Solution:

Let say  Triangle ABC

∠A +  ∠B + ∠C  = 180°

( Sum of angles of triangle )

Let take Exterior angle of  ∠A

Then  Exterior angle of  ∠A  +  ∠A  = 180°  as Linear pair

Equate  180°

Exterior angle of  ∠A  +  ∠A  = ∠A +  ∠B + ∠C

=> Exterior angle of  ∠A  =   ∠B + ∠C

Similarly it can be shown

Exterior angle of  ∠B  =   ∠A + ∠C

Exterior angle of  ∠C  =   ∠A + ∠B

Hence Proved  Exterior angle of triangle is equal to sum of two opposite interior angles  

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