Question

prove that the sum of the angles In a triangle is 180degree

Answer 1

Hey there !!


Prove the angle sum property of triangle.


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1st method .

→ Based on alternate interior angles property.


2nd method.


→ Based on the theorem that the exterior angle of a triangle is equal to the sum of its two opposite angles.


3rd method.

→ Based on theorem that the sum of all exterior angle of a polygon is 360° .


✔✔ Hence, it is proved ✅✅.

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THANKS


#BeBrainly.

Answer 2

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 $lm$ 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 $lm$ 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°