Question

Prove that the sum of the angles of a quadrilateral is 360°.

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Answer 1

Step-by-step explanation:

Given :

• A quadrilateral ABCD.

To prove :

• Sum of the angles of a quadrilateral is 360°.

Proof :

Construction :

• Draw a diagonal that divides the quadrilateral into two equal halves.

Thus we have :

1. In ∆ABC , ∠1 + ∠B + ∠3 = 180°
2. In ∆ADC , ∠2 + ∠D + ∠4 = 180°

∵ Angle sum property :

• Sum of all the interior angles in a triangle is equal to 180°.

Adding 1 and 2 :

• ∠1 + ∠B + ∠3 + ∠2 + ∠D + ∠4 = 180° + 180°
• (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°
• ∠A + ∠B + ∠C + ∠D = 360°

∴ Sum of all the angles of a quadrilateral is 360°.

Answer 2

Step-by-step explanation:

$\large \bold \pink{Question \: \mapsto}$

★ Prove that the sum of the angles of a quadrilateral is 360°.

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$\large \bold \pink{Answer \: \mapsto}$

⟹ To Prove :-

• The sum of all angles of quadrilateral is = 360°

$\large{ \underline \mathfrak \red{Solution \: \mapsto}}$

⟹ As We Know,

• Sum of all angles of n-sided polygon = 180° ( n-2 )
• Here n is the number of side of the Polygon.

⟹ Now,

• A Quadrilateral is a polygon with 4 sides.

⟹ So,

⠀⠀⠀⠀⠀⠀⠀Sum of Angel will be

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 180° [ 4 - 2 ]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 180° × 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\large\fbox\red{= 360°}$

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$\large \green{ \fcolorbox{gray}{black} {\textbf{ Hence, Proved ✔ }}}$

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$\large\colorbox{pink}{Hope lt'z Help You ❥ }$