△ABC da $\angle BAC = 40^{\circ}$ berilgan. $AB$ uzaytmasi $BD$ bo‘lib, $\angle ABD = 120^{\circ}$ (tashqi burchak). $\angle ABC$ va $\angle ACB$ ichki burchaklar bo‘lsin. $\angle ACB$ ning o‘lchamini toping.
- A. $100^{\circ}$
- B. $70^{\circ}$
- C. $80^{\circ}$
- D. $90^{\circ}$
Javob va yechimni ko‘rish
Javob: $80^{\circ}$
$\angle BAC=40^{\circ}$ bo‘lsa, uchburchakning ichki burchaklari yig’indisi $180^{\circ}$ ga teng, ya’ni
\[
\angle ABC+\angle ACB=180^{\circ}-40^{\circ}=140^{\circ}. \tag{1}
\]
$AB$ ning uzaytmasida $\angle ABD=120^{\circ}$ tashqi burchak bo‘lgani uchun, bu burchak $\angle ABC$ ning ichki burchagini to‘ldiradi:
\[
\angle ABD = 180^{\circ}-\angle ABC \;\Longrightarrow\; \angle ABC = 180^{\circ}-120^{\circ}=60^{\circ}. \tag{2}
\]
(2)-ni (1) ga qo‘ysak,
\[
60^{\circ}+ \angle ACB = 140^{\circ}\;\Longrightarrow\; \angle ACB = 80^{\circ}.
\]
Shunday qilib, $\angle ACB$ ning o‘lchami **$80^{\circ}$** bo‘ladi. (Javob: C).