Question

find the sum of all the interior angles of a quadrilateral ABCD using properties of triangle​

Answer 1

Answer:

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Answer 2

Answer:

360°

Step-by-step explanation:

every quadrilateral comprises of two triangles divided by a diagonal... like in the above example of quad. ABCD, diagonal DB divides it into ∆DCB and ∆ADB

the sum of all interior angles of a triangle is 180°

⇒ sum of angles of ∆DCB and ∆ADB = 180° + 180° = 360°

⇒ ∠DCB + ∠CDB + ∠CBD + ∠DAB + ∠ADB + ∠ABD = 360°

⇒ ∠BCD + ∠ADC + ∠DAB + ∠ABC = 360°

⇒ sum of all interior angles of a quadrilateral is 360°