Question

83 If the angles of quadrilateral are
in the ratio 3.5:9:13 then
all angles of quadrilateral are!​

Answer 1

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Answer 2

Given :

• Shape = Quadrilateral
• Ratio of angles of a Quadrilateral are 3:5:9:13.

To Find :

• All the angles of the Quadrilateral.

Solution :

✰ As we know that, Sum of all the angles of a Quadrilateral is 360° (angle sum property of quadrilateral) this means, ∠1 + ∠2 + ∠3 + ∠4 = 360°. Now in this question, ratio is angles are given so we will assume them as follow :

⠀⠀⠀

➟ Let 1st angle be 3x

➟ Let 2nd angle be 5x

➟ Let 3rd angle be 9x

➟ Let 4th angle be 13x

⠀⠀⠀

According to the Question :

⠀⠀⠀⟼⠀⠀⠀∠1 + ∠2 + ∠3 + ∠4 = 360°

⠀⠀⠀⟼⠀⠀⠀3x + 5x + 9x + 13x = 360°

⠀⠀⠀⟼⠀⠀⠀8x + 22x = 360°

⠀⠀⠀⟼⠀⠀⠀30x = 360°

⠀⠀⠀⟼⠀⠀⠀x = 360° / 30

⠀⠀⠀⟼⠀⠀⠀x = 12°

⠀⠀

Therefore :

⇢ First angle = 3x

⇢ First angle = 3 × 12

⇢ First angle = 36°

⠀⠀

⇢ Second angle = 5x

⇢ Second angle = 5 × 12

⇢ Second angle = 60°

⠀⠀

⇢ Third angle = 9x

⇢ Third angle = 9 × 12

⇢ Third angle = 108°

⠀⠀

⇢ Fourth angle = 13x

⇢ Fourth angle = 13 × 12

⇢ Fourth angle = 156°

⠀⠀

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