Question

If the measure of three angle of a quadrilateral are
84°, 67° and 131º find the measure of fourth angle.​

Answer 1

Given : The measure of three angle of a quadrilateral are 84°, 67° and 131º.

Need To Find : Measures of fourth angles of Quadrilateral.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider measure of fourth angle of quadrilateral be x respectively.

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{  84 + 67 + 131 + x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  151 + 131 + x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  282 + x =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  x =\:360-282}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 78\:\degree}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:\:fourth\:angle \:of\:Quadrilateral \:is\bf{\:78\degree \: }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{  84\degree + 67\degree + 131\degree+ 78\degree =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{  282\degree + 78\degree =\:360\degree}$

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

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

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Answer 2

Answer:

fourth angle is -

Step-by-step explanation:

A+B+C=360 A+A+C=360 2A+C=360 2A+131=360 A+131=360/2 A+131=180 A=180-131 A=49