Question

The angle of a quadrilateral are in ratio 2:4:5:7 . Find Measure of all four angle of Quadrilateral

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Answer 1

❍ Let's Consider measure of all four angles of quadrilateral be 2x , 4x ,5x , & 7x .

$\frak{\underline { \dag As \: We \:Know \:that \:,}}$

• $\underline {\boxed {\sf{ \star The \:sum\:of \:all\:angles \:of\:Quadrilateral \:is \:360\degree}}}$

Or ,

• $\underline {\boxed {\sf{ \star \angle A + \angle B + \angle C + \angle D =\:360\degree}}}$

Where ,

• $\angle A , \angle B , \angle C \:and\: \angle D$ are the all four angles of Quadrilateral.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 2x + 4x + 5x + 7x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 6x + 5x + 7x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 11x + 7x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 18x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x =\:\dfrac{\cancel {360}}{\cancel {18}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 20\:\degree}}}}\:\bf{\bigstar}$

Therefore,

• First Angle of Quadrilateral is 2x = 2 × 20 = 40⁰

• Second angle of Quadrilateral is 4x = 4 × 20 = 80⁰

• Third angle of Quadrilateral is 5x = 5 × 20 = 100⁰

• Fourth Angle of Quadrilateral is 7x = 7 × 20 = 140⁰

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:four\:angles \:of\:Quadrilateral \:are\:\bf{40\degree, \:80\degree ,\:100\degree \:and\:140\degree} \: }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed{\sf{\mid{\overline {\underline {\star Verification \::}}}\mid}}}$

$\frak{\underline { \dag As \: We \:Know \:that \:,}}$

• $\underline {\boxed {\sf{ \star The \:sum\:of \:all\:angles \:of\:Quadrilateral \:is \:360\degree}}}$

Or ,

• $\underline {\boxed {\sf{ \star \angle A + \angle B + \angle C + \angle D =\:360\degree}}}$

Where ,

• $\angle A , \angle B , \angle C \:and\: \angle D$ are the all four angles of Quadrilateral.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 100\degree + 80\degree + 40\degree+ 140\degree =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 1 80\degree + 180\degree =\:360\degree}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  360\degree = 360\:\degree}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀