Question

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

Answer 1

Given :

• Angles of a Quadrilateral are in the ratio 3:5:9:13 .

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To Find :

• Find all the angles of the Quadrilateral .

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Solution :

~ Concept Used :

• Angle Sum Property :

${\color{darkblue}{\bigstar}} \: {\underline{\boxed{\orange{\sf{ Sum \; of \; angles {\small_{(Quadrilateral)}} = 360° }}}}} \; {\color{darkblue}{\bigstar}}$

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~ Let the Ratios :

• ∠1 = 3x
• ∠2 = 5x
• ∠3 = 9x
• ∠4 = 13x

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~ Calculating the Value of x :

$\; \; {\dashrightarrow{\qquad{\sf{ ∠1 + ∠2 + ∠3 + ∠4 = 360° }}}}$

$\; \; {\dashrightarrow{\qquad{\sf{ 3x + 5x + 9x + 13x = 360° }}}}$

$\; \; {\dashrightarrow{\qquad{\sf{ 8x + 22x = 360° }}}}$

$\; \; {\dashrightarrow{\qquad{\sf{ 30x = 360° }}}}$

$\; \; {\dashrightarrow{\qquad{\sf{ x = \dfrac{360}{30} }}}}$

$\; \; {\dashrightarrow{\qquad{\sf{ x = \cancel\dfrac{360}{30} }}}}$

$\qquad \; \; {\color{cyan}{:\implies{\underline{\boxed{\red{\sf{ Value \: of \: x \: = 12 }}}}}}}$

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~ Calculating the Angles :

• ➟ ∠1 = 3x = 3(12) = 36°
• ➟ ∠2 = 5x = 5(12) = 60°
• ➟ ∠3 = 9x = 9(12) = 108°
• ➟ ∠4 = 13x = 13(12) = 156°

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~ Therefore :

❝ Angles of the Quadrilateral are 36° , 60° , 108° and 156° . ❞

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Answer 2

Answer:

Solution is in the attachment.

hope it helps you!