Question

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

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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Explanation :-

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

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➻ As we know ,

• The sum of the Angles of a Quadrilateral is 360° .

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➻ According to the question ,

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➳ 3x + 5x + 9x + 13x = 360°

➳ ( 3x + 5x ) + ( 9x + 13x ) = 360°

➳ ( 8x ) + ( 22x ) = 360°

➳ 30x = 360°

➳ x = 360 / 30

➳ x = 12 °

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∴ The Angles are :-

• 3x = 3 × 12 = 36°
• 5x = 5 × 12 = 60°
• 9x = 9 × 12 = 108°
• 13x = 13 × 12 = 156°

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Hence :-

• Angles are 36° , 60° , 108° , 156°

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

Answer 2

Answer:

36 degree,60 degree,108 degree,156 degree

Step-by-step explanation:

a quadrilateral internal angles sum is 360 degree

on adding the ratios given in question we get:30

360 divided by 30=12

ang 1= 12*3=36

ang 2=12*5=60

ang 3=12*9=108

ang 4=12*13=156