Question

Prove that the sum of all the angles of a quadrilateral is 360°​

Answer 1

Answer:

We know that the sum of the angles of a triangle is 180°. ⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)]. Hence, the sum of all the four angles of a quadrilateral is 360°.

Answer 2

Answer:

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Draw any Quadrilateral ABCD . Divide it into two triangles by drawing diagonal . You get six angles i.e ∆1 , ∆2 , ∆3 , ∆4 , ∆B , ∆D .

Use angle sum property of a triangle to find the sum of angles of each triangle .

In ∆ACD , ∆1 + ∆2 + ∆D = 180°

In ∆ABC , ∆3 + ∆4 + ∆B = 180°

Adding corresponding sides of (i) & (ii) , we get

(∆1 + ∆3 + ∆2 + ∆4) + ∆B + ∆D = 180° + 180°

∆A + ∆C + ∆B + ∆D = 360°

-------› ∆A + ∆B + ∆C + ∆D = 360°

Sum of angles of a Quadrilateral is 360° or four right angles .

Step-by-step explanation:

$\huge\mathfrak\pink{i \: hope}\purple{ \: it \: helps} \:$

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