Question

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

Answer 1

To Find,

• All angles of a quadrilateral

Solution,

Given that,

• The angles of a quadrilateral are in the ratio of 3 : 5 : 9 : 13

Figure,

• Refer the attachment.

As we know that,

Sum of all angles of quadrilateral = 360°, First we need to find out the value of x.

➧ 3x + 5x + 9x + 13x = 360

➧ 8x + 9x + 13x = 360

➧ 17x + 13x = 360

➧ 30x = 360

➧ x = 360 / 30

➧ x = 12

The value of x is 12.

The measure of all angles are :-

➧ 3x

= 3 × 12

= 36° ★

➧ 5x

= 5 × 12

= 60° ★

➧ 9x

= 9 × 12

= 108° ★

➧ 13x

= 13 × 12

= 156 ★

Required Answer :

The measure of all angles are :-

• 36°
• 60°
• 108°
• 156°

Answer 2

$\large{\red{\underline{\underline{\textsf{\maltese\:{\red{Given :}}}}}}}$

$\sf{The \:angles \:in \: a \: quadrilateral \: are \:in \:the \: ratio \: 3:5:9:13}$

$\large{\red{\underline{\underline{\textsf{\maltese\:{\red{To\:Find :}}}}}}}$

$\sf{The \:measure \:of \:the \:angles}$

$\large{\red{\underline{\underline{\textsf{\maltese\:{\red{Concept}}}}}}}$

$\sf{All \:the \:angles \:in \:a \: quadrilateral \:add \:upto \:360^0}$

$\large{\red{\underline{\underline{\textsf{\maltese\:{\red{Solution}}}}}}}$

$\sf{Let \:the \:angles \:be \:3x, 5x, 9x \: and \:13x}$

$\sf{So,}$

$\sf{ 3x + 5x + 9x + 13x = 360^0}$

$\sf{30x = 360^0}$

$\sf{x = \dfrac {360^0}{30}}$

$\sf{x = 12^0}$

$\sf{So \:the \:angles \:are:}$

$\sf{3x = 3 \times 12 = 36^0}$

$\sf{5x = 5 \times 12 = 60^0}$

$\sf{9x = 9 \times 12 = 108^0}$

$\sf{13x = 13 \times 12 = 156^0}$