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Question-185283




Question Number 185283 by Mingma last updated on 19/Jan/23
Answered by HeferH last updated on 19/Jan/23
50° ?
$$\mathrm{50}°\:? \\ $$
Commented by Mingma last updated on 20/Jan/23
Can you show your work? The answer is 50
Commented by HeferH last updated on 20/Jan/23
Commented by HeferH last updated on 20/Jan/23
△EAD ∼ △BAC     (by Angle; Angle)    ((EA)/(BA)) = ((DA)/(CA)) ⇒ ((EA)/(DA)) = ((BA)/(CA))    △EAB ∼ △DAC   (by Side; Angle; Side)    ∠ECD = 80°  ∴ α = 50°
$$\bigtriangleup{EAD}\:\sim\:\bigtriangleup{BAC}\:\:\:\:\:\left({by}\:{Angle};\:{Angle}\right)\: \\ $$$$\:\frac{{EA}}{{BA}}\:=\:\frac{{DA}}{{CA}}\:\Rightarrow\:\frac{{EA}}{{DA}}\:=\:\frac{{BA}}{{CA}}\: \\ $$$$\:\bigtriangleup{EAB}\:\sim\:\bigtriangleup{DAC}\:\:\:\left({by}\:{Side};\:{Angle};\:{Side}\right)\: \\ $$$$\:\angle{ECD}\:=\:\mathrm{80}° \\ $$$$\therefore\:\alpha\:=\:\mathrm{50}° \\ $$

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