Question

Prove that the sum of all angles of a quadrilateral is equal to 360.

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Answer 1

To prove :-

• Sum of all angles of a quadrilateral is 360°

Construction :-

• Join BD

Proof :-

→ ∠A + ∠1 + ∠2 = 180° .....(i) [ Sum of angle of Δ ABD ]

→ and ∠3 + ∠C + ∠4 = 180° .....(iii) [ Sum of angle of Δ BCD ]

On adding (i) and (ii), we get

→ ∠A + ∠C + (∠1 + ∠3) + (∠2 + ∠4) = 360°

→ ∠A + ∠C + ∠B + ∠D = 360°

[ °.° ∠1 + ∠3 = ∠B and ∠2 + ∠4 = ∠A ]

→ ∠A + ∠B + ∠C + ∠D = 360°

Hence,proved.

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More details :-

Various types of Quadrilaterals :-

• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium
• Isosceles trapezium
• Kite