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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

$${If}\:``{I}''\:{is}\:{the}\:{incenter},\:{find}\:{x} \\ $$

Answered by mr W last updated on 02/Jan/23

Commented by mr W last updated on 02/Jan/23

3α=180−A−(B/2)  3β=180−B−(A/2)  ⇒3(α+β)=360−((3(A+B))/2)  ⇒α+β=120−((A+B)/2)   ...(I)  α+β+x=180−((A+B)/2)   ...(II)  ⇒x=60° ✓

$$\mathrm{3}\alpha=\mathrm{180}−{A}−\frac{{B}}{\mathrm{2}} \\ $$$$\mathrm{3}\beta=\mathrm{180}−{B}−\frac{{A}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{3}\left(\alpha+\beta\right)=\mathrm{360}−\frac{\mathrm{3}\left({A}+{B}\right)}{\mathrm{2}} \\ $$$$\Rightarrow\alpha+\beta=\mathrm{120}−\frac{{A}+{B}}{\mathrm{2}}\:\:\:...\left({I}\right) \\ $$$$\alpha+\beta+{x}=\mathrm{180}−\frac{{A}+{B}}{\mathrm{2}}\:\:\:...\left({II}\right) \\ $$$$\Rightarrow{x}=\mathrm{60}°\:\checkmark \\ $$

Answered by Acem last updated on 02/Jan/23

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