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Question Number 215723 by OsamaWafa last updated on 16/Jan/25

Answered by som(math1967) last updated on 16/Jan/25

Commented by som(math1967) last updated on 16/Jan/25

∠AEC=180−130=50[ABCE cyclic] ∠CAE=180−110=70[ACDEcyclic] from △ACE x=180−50−70=60

$$\angle{AEC}=\mathrm{180}−\mathrm{130}=\mathrm{50}\left[{ABCE}\:{cyclic}\right] \\ $$$$\angle{CAE}=\mathrm{180}−\mathrm{110}=\mathrm{70}\left[{ACDEcyclic}\right] \\ $$$${from}\:\bigtriangleup{ACE}\: \\ $$$$\:{x}=\mathrm{180}−\mathrm{50}−\mathrm{70}=\mathrm{60} \\ $$

Answered by A5T last updated on 16/Jan/25

Commented by A5T last updated on 16/Jan/25

∠CBE=180°−110°=70° since BCDE is cyclic ⇒x=130°−∠CBE=60°

$$\angle\mathrm{CBE}=\mathrm{180}°−\mathrm{110}°=\mathrm{70}°\:\mathrm{since}\:\mathrm{BCDE}\:\mathrm{is}\:\mathrm{cyclic} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{130}°−\angle\mathrm{CBE}=\mathrm{60}° \\ $$

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