Question

Three angles of a quadrilateral are equal then the measure of the fourth angle is 120. Find the measure of each of the equal angles.​

Answer 1

Hope this answer helps you....!!!

Answer 2

❍ Let's Consider all three angles of quadrilateral be x .

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x + x + x + 120⁰ =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 2x + x + 120 =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 3x + 120 =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 3 x =\:360\degree - 120\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 3 x =\:240\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ x =\:\dfrac{\cancel {250}}{\cancel {3}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 80\:\degree}}}}\:\bf{\bigstar}$

Thus,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence,\: Measure \:of\:all\:each\:equal\:angles \:of\:Quadrilateral \bf{\: \:80\degree } \: }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

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

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

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.

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

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 80\degree + 80\degree + 80\degree+ 120\degree =\:360\degree}$

⠀⠀⠀⠀⠀⠀$:\implies \tt{ 240\degree + 120\degree =\:360\degree}$

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

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

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀