Question

the angles of the quardiletral are in the ratio 3:5:9:13. Find all the angles of the quardiletral​

Answer 1

Answer :-

• The angles of the quadrilateral are 36°, 60°, 108° and 156°.

Given :-

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

To find :-

• All the angles of the quadrilateral.

Step-by-step explanation :-

• It has been given that the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13.

• So, let the angles be 3x, 5x, 9x and 13x.

Now, we know that :-

$\underline{\boxed{\sf Sum \: of \: all \: angles \: in \: a \: quadrilateral = 360^{\circ}.}}$

So, the sum of 3x, 5x, 9x and 13x should be equal to 360°.

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$\implies\sf3x + 5x + 9x + 13 = 360^{\circ}$

Adding all the variable terms,

$\implies \sf30x = 360^{\circ}$

Transposing 30 from LHS to RHS, changing it's sign,

$\implies \sf x = \dfrac{360^{\circ}}{30}$

Dividing 360° by 30,

$\implies\sf x = 12^{\circ}.$

• The value of x is 12°.

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Hence, the value of all the angles are as follows :-

$\bf3x = 3 \times 12^{\circ} = 36^{\circ}$

$\bf5x = 5 \times 12^{\circ} = 60^{\circ}$

$\bf9x = 9 \times 12^{\circ} = 108^{\circ}$

$\bf13x = 13 \times 12^{\circ} = 156^{\circ}$

Answer 2

Question:-

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

Required Answer:-

Given:-

$\sf{\rightarrow{The \: angles\:of\:a\: quadrilateral \: 3:5:9:13}}$

To Find:-

$\sf{\rightarrow{All\:the\:angles\:of\:the\:quadrilateral}}$

Solution:-

Let all the angles be a,b,c,d respectively.

Let,

a = 3x

b = 5x

c = 9x

d = 13x

Where x can be any number.

As we know that,

$\boxed{\blue{\sf{The \: sum \: of \: all \: angles \: of \: a \: quadrilateral =360 \degree}}}$

According to the question,

$\sf{\bold{a + b + c + d = 360\degree}}$

Substituting the values,

$\\ \sf{\implies{3x + 5x + 9x + 13x = 360\degree}}$

$\\ \sf{\implies{30x = 360\degree}}$

$\\ \sf{\implies{x = \frac{360}{30} }}$

$\\ \sf{\therefore{\bold{x = 12\degree}}}$

Now, by substituting the value of x , we find:-

$\sf{\bold{a}} = 3 \times 12 = \orange{36\degree }\\\sf{\bold{b}} = 5 \times 12 =\orange{ 60{\degree}} \\ \sf{\bold{c}} = 9 \times 12 = \orange{108\degree} \\ \sf{\bold{d}} = 13 \times 12 =\orange{ 156\degree}$

$\underline{\boxed{\rm{Hence,the \: value \: of \: all \: angles \: are \: \bold{ 30\degree 60 \degree 108\degree and 156 \degree}}}}$