Question

The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the triangle.​

Answer 1

Question :-

• The Angles of Quadrilateral are in the ratio 3 : 5 : 9 : 13 . Find all the Angles of the Quadrilateral .

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Answer :-

• The Angles of Quadrilateral are 36° , 60° , 108° and 156° .

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Given :-

• Ratio of Angles of Quadrilateral are 3 : 5 : 9 : 13

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To Find :-

• Angles of the Quadrilateral .

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Solution :-

• Here, Ratio of Angles of Quadrilateral are given 3 : 5 : 9 : 13 . And, we have to find Angles of Quadrilateral .

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➻ Theorem :-

• By Angle Sum Property, The sum of the Angles of a Quadrilateral is 360°

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➻ According to the question :-

$\Longrightarrow \: \: \sf{3x \: + \: 5x \: + \: 9x \: + \: 13x \: = \: 360}$

$\Longrightarrow \: \: \sf{30x \: = \: 360}$

$\Longrightarrow \: \: \sf{x \: = \: \frac{360}{30} }$

$\Longrightarrow \: \: \sf{x \: = \: 12 \degree}$

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➻ By finding the Angles :-

$\Longrightarrow \: \: \sf{3x = 3 \times 12 = 36 \degree}$

$\Longrightarrow \: \: \sf{5x = 5 \times 12 = 60\degree}$

$\Longrightarrow \: \: \sf{9x = 9 \times 12 = 108\degree}$

$\Longrightarrow \: \: \sf{13x = 13 \times 12 = 156\degree}$

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Hence :-

• Angles of Quadrilateral = 36° , 60° , 108° and 156° .

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$\begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \pmb {\sf \red{ \dag \: \: More \: Information \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \sf{Sum \: of \: Angles \: of \: Triangle = 180 \degree} \\ \\ \\ \footnotesize \bigstar \: \sf{Sum \: of \: Angles \: of \: Pentagon = 540 \degree} \\ \\ \\ \footnotesize \bigstar \: \sf{Sum \: of \: Angles \: of \: Hexagon = 720 \degree} \\ \\ \\ \footnotesize \bigstar \: \sf{Sum \: of \: Angles \: of \: Heptagon = 900 \degree} \\ \\ \\ \footnotesize \bigstar \: \sf{Sum \: of \: Angles \: of \: Octagon = 1080 \degree}\end{array}}\end{gathered}\end{gathered}$