the angles of a quadrilateral are in the ratio 3 ratio 5 ratio 9 ratio 13 ratio find all the angle of the quadrilateral ​

2 thoughts on “the angles of a quadrilateral are in the ratio 3 ratio 5 ratio 9 ratio 13 ratio find all the angle of the quadrilateral ​”

1. Given: The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13

   To Be Found: The measures of all the angles in the quadrilateral

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   ❍ Let the angles in the quadrilateral be 3x, 5x, 9x and 13x

   [tex]{ \underline{\bigstar{ \bf{ As \: we \: know \: that: }}}}[/tex]

   • The sum of measures of all the angles in a quadrilateral equals 360°⠀⠀⠀

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   ⠀⠀⠀⠀⠀⠀☆ Let’s frame an equation according stating that the sum of the agles in the quadrilateral is 360°

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   [tex]{ \underline{ \bigstar \: { \textbf{Framing an equation we get : }}}}[/tex]

   [tex] \\ : \implies \sf \: 3x + 5x + 9x + 13x = 360 \\ \\ \\ : \implies \sf \: 8x + 9x + 13x = 360 \\ \\ \\ : \implies \sf \: 17x + 13x = 360 \\ \\ \\ : \implies \sf \: 30x = 360 \\ \\ \\ : \implies \sf \: x = \cancel\frac{360}{30} \\ \\ \\ : \implies \sf { \purple{ \underline{ \boxed{ \pmb{ \frak{x = 12}}}} \bigstar}}[/tex]

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   ⠀⠀⠀⠀⠀⠀☆ Now, let’s find the measures of the angles in the quadrilateral as the assumptions we made

   ⠀⠀⠀⠀⠀⠀⠀⠀▪⠀3x = 3(12) = 36°

   ⠀⠀⠀⠀⠀⠀⠀⠀▪⠀ 5x = 5(12) = 60°

   ⠀⠀⠀⠀⠀⠀⠀⠀▪⠀9x = 9(12) = 108°

   ⠀⠀⠀⠀⠀⠀⠀⠀▪⠀13x = 13(12) = 156°

   Therefore, ⠀

   [tex]{\purple{\underline{\sf{ the \: measures \: of \: the \: angles \: are : 36,60,108,156\: degrees}}}}[/tex]

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2. Answer:

   Let the ratio be 3x:5x:9x:13x.

   According to the angle sum property of quadrilateral, the sum of all four angles is 360°.

   => 3x + 5x + 9x + 13x = 360°

   => 30x = 360°

   => x = 360/30

   => x = 12

   Therefore, the angles are 36°, 60°, 108° and 156°.

   Reply