Question

if the angles of quadrilateral are in the ratio 1:2:3:4 find all the angles ​

Answer 1

Answer:

36⁰, 72⁰, 108⁰, 144⁰

Step-by-step explanation:

x + 2x + 3x + 4x = 360

10x = 360

x = 36

2x = 2*36 = 72

3x = 3*36 = 108

4x = 4*36 = 144

Answer 2

Given : The angles of Quadrilateral is in ratio 1:2:3:4 .

Need To Find : Measures of all angles of Quadrilateral.

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❍ Let's Consider measure of all four angles of quadrilateral be 1x , 2x ,3x , & 4x .

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{  1x + 2x + 3x + 4x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  3x + 3x + 4x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  6x + 4x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  10x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x =\:\dfrac{\cancel {360}}{\cancel {10}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 36\:\degree}}}}\:\bf{\bigstar}$

Therefore,

• First Angle of Quadrilateral is x = = 36⁰

• Second angle of Quadrilateral is 2x = 2 × 36 = 72⁰

• Third angle of Quadrilateral is 3x = 3 × 36 = 108⁰

• Fourth Angle of Quadrilateral is 4x = 4 × 20 = 144⁰

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:four\:angles \:of\:Quadrilateral \:are\:36\degree, \:72\degree ,\:108\degree \:and\:144\degree \: }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{  36\degree + 72\degree + 108\degree+ 144\degree =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  216\degree + 144\degree =\:360\degree}$

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

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

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