Question Number 184199 by HeferH last updated on 03/Jan/23
Commented by HeferH last updated on 03/Jan/23
$${if}\:{E}\:{is}\:{the}\:{excenter}\:{of}\:{ABC},\:{find}\:{x}\: \\ $$
Answered by mr W last updated on 04/Jan/23
Commented by mr W last updated on 04/Jan/23
$$\Delta{DEF}\equiv\Delta{BEG} \\ $$$$\Rightarrow{DE}={BE} \\ $$$$\Rightarrow\angle{DBE}={x} \\ $$$$\Rightarrow\angle{DBC}={x}−\alpha=\mathrm{180}−\mathrm{40}−\left({x}+\alpha\right) \\ $$$$\mathrm{2}{x}=\mathrm{140} \\ $$$$\Rightarrow{x}=\mathrm{70}°\:\checkmark \\ $$
Commented by HeferH last updated on 04/Jan/23
$${Thank}\:{you},\:{I}\:{got}\:{the}\:{same}\:{answer}\:{but}\:{on}\:{the} \\ $$$$\left.\:{book}\:{says}\:{x}\:=\:\mathrm{50}°,\:{I}\:{guess}\:{it}\:{was}\:{a}\:{typo}\::\right)\: \\ $$$$\left.\:\left.\left({option}\:{B}\right)\:\mathrm{70}°,\:{option}\:{D}\right)\:\mathrm{50}°\right) \\ $$
Commented by mr W last updated on 05/Jan/23
$${x}=\mathrm{70}°\:{is}\:{right}.\:{book}\:{is}\:{wrong}. \\ $$