Question

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

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

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

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

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

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

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

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

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

$\sf{So,}$

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

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

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

$\sf{x = 12^0}$

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

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

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

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

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

Answer 2

Let, angles of the quadrilateral be 13x, 9x, 5x and 3x.

We know, sum of interior angles of a quadrilateral = 360°

∴ 13x + 9x + 5x + 3x = 360°

⇒ 30x = 360°

⇒ x = 360°/30

⇒ $\boxed{x = 12°}$.

Putting the values,

Angle 1: 13x = 13(12°) = 156°

Angle 2: 9x = 9(12°) = 108°

Angle 3: 5x = 5(12°) = 60°

Angle 4: 3x = 3(12°) = 36°.

(After adding the angle measurements, you'll get 360° - verification).

More about a quadrilateral and it's types:-

1. Quadrilateral (meaning, 4 sides) is a plane figure having 4 sides. All the interior angles make 360°. This can be proved by breaking it into two triangles.

2. Quadrilaterals are of several types, viz., Rectangle, Square, Kite, Rhombus, Parallelogram, Cyclic, Trapezoid, etc.