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Four-sides-mAB-mBC-mCD-and-mDA-of-a-quadrilateral-ABCD-have-measurement-a-b-c-and-d-units-respectively-Let-the-sum-of-any-adjacent-sides-is-not-equal-to-the




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

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