Question

prove that the sum of the four angles of a quadrilateral is 360°​

Answer 1

To prove :-

that the sum of the four angles of a quadrilateral is 360°

Construction :-

Join AC

Proof :-

We know that sum of the angle in triangle is equal to 180°

So, In ∆ABC

∠2 + ∠4 + ∠B = 180° .........(1)

Similarly,

In ∆ACD, we have

∠1 + ∠3 + ∠D = 180° ..........(2)

Now adding (1) and (2)

➝ ∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 180° + 180°

➝ ∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360°

here,

∠1 + ∠2 = ∠A and ∠3 + ∠4 = ∠C

So,

➝ (∠2 + ∠4) + ∠B + (∠1 + ∠3) + ∠D = 360°

➝ ∠A + ∠B + ∠C + ∠D = 360°

${ \large{ \bf{Hence \: proved \: !}}}$

Answer 2

Answer:

Thanks for the answer