Question

22. the angles of quadrilateral are in the ratio 3:5:9:13. find all the angles of the quadrilateral.​

Answer 1

Answer:

The angles are 36°, 60°, 108°, 156°.

Answer 2

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

Need To Find: All the angles of Quadrilateral.

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

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

Sum of all angles of a Quadrilateral is 360°

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Let a = 3x , b = 5x , c = 9x , d = 13x.

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$~~~~{\underline{\bf{\dag}{\frak{\pink{ \: \: Substituting \: the \: values \: }}}}}$

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$\begin{gathered}\: :\implies\sf a + b + c + d = {360}^{\circ}\\\\\\ :\implies\sf3x \: + \: 5x \: + \: 9x + 13x \: = {360}^{\circ}\\\\\\ :\implies\sf \: 30x \: = \: {360}^{\circ}\\\\\\ :\implies\sf \: x \: = \dfrac{ {360}^{ \circ} }{30}\\\\\\ :\implies{ \boxed{\sf{\orange{ x \: = \: {12}^{ \circ}}}}} \end{gathered}$

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Similarly, The angles are:

⠀⠀⠀⠀$\sf{a = 3x = 3 \times {12}^{ \circ} = {36}^{ \circ}}$

⠀⠀⠀⠀$\sf{b = 5x = 5 \times\: {12}^{ \circ} = {60}^{ \circ}}$

⠀⠀⠀⠀$\sf{c = 9x = 9 \times\;{12}^{ \circ} = {108}^{ \circ}}$

⠀⠀⠀⠀$\sf{d = 13x = 13 \times {12}^{ \circ} = {156}^{ \circ}}$

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