The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (

1.	The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (1/2)∠BAC, then what is the value of ∠BAC ?
Answer» $\huge\sf\red{Given\::}$ $\sf \angle ACD\: = \:114\degree$ $\sf \angle ABC\:=\:\dfrac{1}{2}\:\angle BAC$ $\huge\sf\blue{To\:Find\::}$ $\sf The\: value\: of \:\angle BAC$ $\huge\sf\purple{Solution\::}$ $\sf Let,$ $\sf \angle ABC \: = \: x$ $\sf \angle BAC \:=\: 2x$ $\sf\underline{Now,\:By\:using\: exterior\: angle\: property}$ $\longrightarrow\:\:\sf \angle BAC \:=\:\angle ABC \:=\: \angle ACD$ $\longrightarrow\:\:\sf 2x\:+\:x\:=\:144\degree$ $\longrightarrow\:\:\sf 3x\:=\:144\degree$ $\longrightarrow\:\:\sf x\:=\:\dfrac{\cancel{144\degree}}{\cancel{3}}$ $\longrightarrow\:\:\sf x\:=\:38\degree$ $\sf Put \:the\:x\: value\:in\:\angle BAC$ $\longrightarrow\:\:\sf 2\:\times\:38\degree$ $\longrightarrow\:\:\sf 76\degree$ $\sf\star\:\:\underline\pink{Hence, \:\angle BAC\:is\:76\degree}$