the angles of a quadrilateral are in the ratio 1:3:5:6 find its greatest angle​

2 thoughts on “the angles of a quadrilateral are in the ratio 1:3:5:6 find its greatest angle​”

1. Step-by-step explanation:

   Answer in full explanation:–

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   1x +3x + 5x + 6x = 360

   15x = 360

   x = 360/15

   x = 24

   6x = 24 × 6

   = 144

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2. [tex]\large {\pmb{\mathfrak{☆ \: Given:}}}[/tex]

   The angles of a quadrilateral are in the ratio of 1:3:5:6.

   [tex] \\ [/tex]

   [tex]\large {\pmb{\mathfrak{☆ \: \: To \: find:}}}[/tex]

   We have to find the greatest angle in the quadrilateral.

   [tex] \\ [/tex]

   [tex]\large {\pmb{\mathfrak{☆ \: \: Solution: }}}[/tex]

   We know that, sum of all the angles in a quadrilateral = 360°.

   Let the unknown constant be x.

   [tex]\sf :\implies x+3x+5x+6x=360\degree[/tex]

   [tex]\sf :\implies 15x=360\degree[/tex]

   [tex]\sf :\implies x= \dfrac{360\degree}{15} [/tex]

   [tex]\boxed{\pmb{\sf {\therefore \: x=24\degree}}}[/tex]

   Now, substituting x = 24° in the ratios :

   [tex]\sf :\implies \measuredangle1: \pmb{\sf x=24\degree}[/tex]

   [tex]\sf :\implies \measuredangle2:{\pmb{\sf{3x=3(24\degree)=72\degree}}}[/tex]

   [tex]\sf :\implies \measuredangle3:{\pmb{\sf{5x=5(24\degree)=120 \degree}}}[/tex]

   [tex]\sf :\implies \measuredangle4:{\pmb{\sf{6(24\degree)=144 \degree}}}[/tex]

   [tex]\boxed{\pmb{\sf{\therefore \: Greatest \: angle =144\degree}}}[/tex]

   [tex] \\ [/tex]

   [tex]\large {\pmb{\mathfrak{☆ \: \: Verification:}}}[/tex]

   Let’s verify whether the angles add upto 360° or not :

   [tex]\sf :\implies x+3x+5x+6x=360\degree[/tex]

   [tex]\sf :\implies 24\degree+3(24\degree)+5(24\degree)+6(24\degree)=360[/tex]

   [tex]\sf :\implies 24\degree+72\degree+120 \degree + 144 \degree = 360 \degree[/tex]

   [tex]\sf:\implies 96\degree+264 \degree = 360 \degree[/tex]

   [tex]\sf :\implies {360\degree=360\degree}[/tex]

   [tex]\boxed{\pmb{\sf{Hence, ~ verified!}}}[/tex]

   [tex] \\ [/tex]

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