Question Number 1378 by Rasheed Soomro last updated on 28/Jul/15
$$\:\:\:\:\:{Four}\:{sides}\:{m}\overline {\boldsymbol{\mathrm{AB}}}\:,\:{m}\overline {\boldsymbol{\mathrm{BC}}}\:,\:{m}\overline {\boldsymbol{\mathrm{CD}}}\:\:{and}\:\:{m}\overline {\boldsymbol{\mathrm{DA}}}\:{of}\:{a}\:\boldsymbol{\mathrm{quadrilateral}}\: \\ $$$$\boldsymbol{\mathrm{ABCD}}\:\:{have}\:{measurement}\:\boldsymbol{{a}}\:,\:\boldsymbol{{b}}\:,\:\boldsymbol{{c}}\:\:{and}\:\boldsymbol{{d}}\:{units}\:{respectively}. \\ $$$$\:\:\:\:\:{Let}\:{the}\:{sum}\:{of}\:{any}\:{adjacent}\:{sides}\:{is}\:{not}\:{equal}\:{to}\:{the}\:{sum}\:{of} \\ $$$${remaining}\:{adjacent}\:{sides}\:\:{and}\:{measurement}\:{of}\:{all}\:{the}\:{sides}\: \\ $$$${is}\:{positive}\:{and}\:{real}. \\ $$$$\:\:\:\:\:\:{What}\:{could}\:{be}\:{the}\:{possible}\:{minimum}\:{and}\:{maximum}\:{values} \\ $$$${of}\:{its}\:{one}\:{angle}\:\:{m}\angle\boldsymbol{\mathrm{A}}\:? \\ $$
Commented by 123456 last updated on 26/Jul/15
$${m}\angle\boldsymbol{\mathrm{A}}+{m}\angle\boldsymbol{\mathrm{B}}+{m}\angle\boldsymbol{\mathrm{C}}+{m}\angle\boldsymbol{\mathrm{D}}=\mathrm{360}° \\ $$
Commented by prakash jain last updated on 27/Jul/15
$${m}\in\mathbb{N}\:\mathrm{and}\:\mathrm{are}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{integers}? \\ $$
Commented by prakash jain last updated on 28/Jul/15
$$\mathrm{All}\:\mathrm{values}\:\mathrm{will}\:\mathrm{be}\:\mathrm{possible}\:\mathrm{except}\:\mathrm{0},\pi,\mathrm{2}\pi. \\ $$
Commented by Rasheed Soomro last updated on 28/Jul/15
$${Sir}\:{you}\:{are}\:{very}\:{right}.\:{What}\:{a}\:{meaningless}\:{question}\:{have} \\ $$$${I}\:{asked}\:!\:{I}\:{am}\:{very}\:{very}\:{sorry}.\:{This}\:{were}\:{not}\:{what}\:{I}\:{should} \\ $$$${have}\:{asked}! \\ $$