Question Number 183991 by HeferH last updated on 01/Jan/23
Commented by HeferH last updated on 01/Jan/23
$${If}\:``{I}''\:{is}\:{the}\:{incenter},\:{find}\:{x} \\ $$
Answered by mr W last updated on 02/Jan/23
Commented by mr W last updated on 02/Jan/23
$$\mathrm{3}\alpha=\mathrm{180}−{A}−\frac{{B}}{\mathrm{2}} \\ $$$$\mathrm{3}\beta=\mathrm{180}−{B}−\frac{{A}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{3}\left(\alpha+\beta\right)=\mathrm{360}−\frac{\mathrm{3}\left({A}+{B}\right)}{\mathrm{2}} \\ $$$$\Rightarrow\alpha+\beta=\mathrm{120}−\frac{{A}+{B}}{\mathrm{2}}\:\:\:...\left({I}\right) \\ $$$$\alpha+\beta+{x}=\mathrm{180}−\frac{{A}+{B}}{\mathrm{2}}\:\:\:...\left({II}\right) \\ $$$$\Rightarrow{x}=\mathrm{60}°\:\checkmark \\ $$
Answered by Acem last updated on 02/Jan/23
