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Question-190563




Question Number 190563 by Best1 last updated on 06/Apr/23
Answered by a.lgnaoui last updated on 06/Apr/23
•1a)∡x et ∡72  interceptent le      meme arc  ; alors                               [x=72]  •1b  x=2y=2×33                                [ x=66]  •1c    p+q=48+32=80  •2a  x+30=90   ⇒[x=60]  •2b   x+45=180⇒[x=135]  •2c     x+(180−110)=90                            ⇒ [x=20]  2•d      (180−110)+90+∡B=180           ⇒∡B=20 =2x            ⇒x=10
$$\left.\bullet\mathrm{1}{a}\right)\measuredangle{x}\:{et}\:\measuredangle\mathrm{72}\:\:{interceptent}\:{le} \\ $$$$\:\:\:\:{meme}\:{arc}\:\:;\:{alors} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{x}}=\mathrm{72}\right] \\ $$$$\bullet\mathrm{1}{b}\:\:{x}=\mathrm{2}{y}=\mathrm{2}×\mathrm{33} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:\boldsymbol{{x}}=\mathrm{66}\right] \\ $$$$\bullet\mathrm{1}{c}\:\:\:\:{p}+{q}=\mathrm{48}+\mathrm{32}=\mathrm{80} \\ $$$$\bullet\mathrm{2}{a}\:\:{x}+\mathrm{30}=\mathrm{90}\:\:\:\Rightarrow\left[\boldsymbol{{x}}=\mathrm{60}\right] \\ $$$$\bullet\mathrm{2}{b}\:\:\:{x}+\mathrm{45}=\mathrm{180}\Rightarrow\left[\boldsymbol{{x}}=\mathrm{135}\right] \\ $$$$\bullet\mathrm{2}{c}\:\:\:\:\:{x}+\left(\mathrm{180}−\mathrm{110}\right)=\mathrm{90} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\left[\boldsymbol{{x}}=\mathrm{20}\right] \\ $$$$\mathrm{2}\bullet{d}\:\:\:\:\:\:\left(\mathrm{180}−\mathrm{110}\right)+\mathrm{90}+\measuredangle{B}=\mathrm{180} \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\measuredangle{B}=\mathrm{20}\:=\mathrm{2}{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\boldsymbol{{x}}=\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

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