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Question-190557




Question Number 190557 by Best1 last updated on 05/Apr/23
Answered by a.lgnaoui last updated on 06/Apr/23
•a)80=2x                ⇒x=40  •b)x=2(180−140) ⇒ x=80  •c)triangle rectangle⇒x=90  •d)     α+β+130=360       (1)                   x+130=α+β     (2)        ⇒x+260= 360    x=100     •e) { ((x+β+2α=180         (1))),((    λ=α+40    [△OBC isocele]   )) :}  △(OAC isocele)⇒   { ((2θ+2(α+40)+(α+β+x)=360 (2))),((2θ+α+x=180          (3))) :}  (2)−(3)⇒2α+β+80=180  ⇒2α+β=100  ⇒(1)⇔x+100=180  ⇒         x=80  [A suivre pour (f)  et (g)]
$$\left.\bullet{a}\right)\mathrm{80}=\mathrm{2}{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow{x}=\mathrm{40} \\ $$$$\left.\bullet{b}\right){x}=\mathrm{2}\left(\mathrm{180}−\mathrm{140}\right)\:\Rightarrow\:{x}=\mathrm{80} \\ $$$$\left.\bullet{c}\right){triangle}\:{rectangle}\Rightarrow{x}=\mathrm{90} \\ $$$$\left.\bullet{d}\right)\:\:\:\:\:\alpha+\beta+\mathrm{130}=\mathrm{360}\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+\mathrm{130}=\alpha+\beta\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\Rightarrow{x}+\mathrm{260}=\:\mathrm{360}\:\:\:\:{x}=\mathrm{100}\:\:\: \\ $$$$\left.\bullet{e}\right)\begin{cases}{{x}+\beta+\mathrm{2}\alpha=\mathrm{180}\:\:\:\:\:\:\:\:\:\left(\mathrm{1}\right)}\\{\:\:\:\:\lambda=\alpha+\mathrm{40}\:\:\:\:\left[\bigtriangleup{OBC}\:{isocele}\right]\:\:\:}\end{cases} \\ $$$$\bigtriangleup\left({OAC}\:{isocele}\right)\Rightarrow \\ $$$$\begin{cases}{\mathrm{2}\theta+\mathrm{2}\left(\alpha+\mathrm{40}\right)+\left(\alpha+\beta+{x}\right)=\mathrm{360}\:\left(\mathrm{2}\right)}\\{\mathrm{2}\theta+\alpha+{x}=\mathrm{180}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{3}\right)}\end{cases} \\ $$$$\left(\mathrm{2}\right)−\left(\mathrm{3}\right)\Rightarrow\mathrm{2}\alpha+\beta+\mathrm{80}=\mathrm{180} \\ $$$$\Rightarrow\mathrm{2}\alpha+\beta=\mathrm{100} \\ $$$$\Rightarrow\left(\mathrm{1}\right)\Leftrightarrow{x}+\mathrm{100}=\mathrm{180} \\ $$$$\Rightarrow\:\:\:\:\:\:\:\:\:{x}=\mathrm{80} \\ $$$$\left[{A}\:{suivre}\:{pour}\:\left({f}\right)\:\:{et}\:\left({g}\right)\right] \\ $$
Commented by a.lgnaoui last updated on 06/Apr/23
Answered by a.lgnaoui last updated on 06/Apr/23
•f) { ((2α+2β+(180−x)=360)),((α+β                             =100)) :}  ⇒200+(180−x)=360                       380−x=360                    x=20  •g)AB=AC   ∡BOC=72    2a=108    (x+y)=36     x=y                         ⇒x=18
$$\left.\bullet{f}\right)\begin{cases}{\mathrm{2}\alpha+\mathrm{2}\beta+\left(\mathrm{180}−{x}\right)=\mathrm{360}}\\{\alpha+\beta\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{100}}\end{cases} \\ $$$$\Rightarrow\mathrm{200}+\left(\mathrm{180}−{x}\right)=\mathrm{360} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{380}−{x}=\mathrm{360} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}=\mathrm{20} \\ $$$$\left.\bullet{g}\right){AB}={AC}\:\:\:\measuredangle{BOC}=\mathrm{72} \\ $$$$\:\:\mathrm{2}{a}=\mathrm{108} \\ $$$$\:\:\left({x}+{y}\right)=\mathrm{36}\:\:\:\:\:{x}={y} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\boldsymbol{{x}}=\mathrm{18} \\ $$
Commented by greg_ed last updated on 06/Apr/23
ok
$$\mathrm{ok} \\ $$

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