Question

the angles of a quadrilateral are in the ratio 3 ratio 5 ratio 9 ratio 13 ratio find all the angle of the quadrilateral ​

Answer 1

Answer:

We know that,

Angle of quadrilateral is 360

Let the angle be x.

1st angle be 3x

2nd angle be 5x

3rd angle be 9x

4th angle be 13x

Now,

3x+5x+9x+13x=360°

30x=360°

x=360/30 =12

1st angle =3x=3×12=36°

2nd angle=5x=5×12=60°

3rd angle=9x=9×12=108°

4tn angle=13x=13×12=156°

Step-by-step explanation:

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Answer 2

Stated - The angles of Quadrilateral are in ratio 3:5:9:13

To Attain - All the angles of the Quadrilateral

⠀⠀⠀⠀⠀____________________

❍ Let the all the angles of quadrilateral be 3x, 5x, 9x, 13x

∠A : ∠B : ∠C : ∠D = 3 : 5 : 9 : 13.

⠀

Let,

∠A = 3, ∠B = 5 , ∠C = 9 ,∠D = 13

⠀

${\underline{\frak{\dag{\pink{\:As \; we \; know \; that:}}}}}$

⠀

⧠ Sum of all angles of quadrilateral is 360°

⠀

⠀⠀⠀⠀$\dag{\underline{\frak{ \pink{ \: Substituting  \: the \:  value : }}}}$

⠀

$\begin{gathered}\rightarrowtail\sf {\angle A + \angle B + \angle C + \angle D = {360}^{\circ}}\\\\\\\rightarrowtail\sf{3x + 5x +  9x+ 13x \: ={360}^{\circ}}\\\\\\\rightarrowtail\sf{30x = {360}^{\circ}}\\\\\\\rightarrowtail \sf\:{x\:=\:\dfrac{{360}^{\circ}}{30}}\\\\\\\rightarrowtail \underline{\boxed{\frak{\pink{x\:= 12}}}}\end{gathered}$

Now,

$\:\:\:\:\twoheadrightarrow$∠A = 3(12) = 36°

$\:\:\:\:\twoheadrightarrow$∠B = 5(12) = 60

$\:\:\:\:\twoheadrightarrow$∠C = 9(12) = 108°

$\:\:\:\:\twoheadrightarrow$∠D = 13(12) = 156°

⠀

C L A R I F I C A T I O N :

⠀$\:\:\:\twoheadrightarrow$∠A + ∠B + ∠C + ∠D = 360°

⠀$\:\:\:\twoheadrightarrow$ 36° + 60° + 108° + 156° = 360°

⠀$\:\:\:\twoheadrightarrow$ 96° + 264° = 360°

⠀$\:\:\:\twoheadrightarrow$ 360° = 360°

⠀$\:\:\:\twoheadrightarrow$ LHS = RHS

⠀

Final Answer -

⠀⠀ ➠ Hence, The measure required angles are 36°, 60°, 108°, 156°.

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