Question

prove that sum of angles of triangle is 180

Answer 1

Statement : The sum of the angles of a triangle is 180°.

To prove : sum of the angles of ΔABC is 180°

Construction : Draw a line parallel to BC.

Proof :

Since lm || BC, we have ;

∠2 = ∠y ..... (i) . [Alternate interior angles]

Similarly,

∠1 = ∠z ....... (ii) . [Alternate interior angles]

Also, sum of angles at a point a on line is 180°.

∴ ∠2 + ∠x + ∠1 = 180°

⇒ ∠y + ∠x + ∠z = 180°

⇒ ∠x + ∠y + ∠z = 180°

⇒ ∠A + ∠B + ∠C = 180°

Therefore,

Sum of all angles of a Δ is 180°

Answer 2

Heya....

Ques :- Prove that sum of angles of triangle is 180.....

Solution ___________

• Draw the line II to BC

Now according to this ...

<2 = <y ( alternate interior angles )

<1 = <z = ( alternate interior angle )

As sum of all the points on line LM is 180°

So______ by using above data :-

<2+<x+<1 = 180°

<y+<x+<z = 180°

<A+<B+<C = 180° Proved ..

Thank you