Given: In a triangle ABC,AB=AC ∠ACD=x Formula Used: The sum of the linear pair of angles =180∘ ∠A+∠B+∠C=180∘ Calculation:
Since, △ABC is an isosceles triangle So, ∠ABC=∠ACB[∵AB=AC]⋯ (i) According to the figure ∠ACB+∠ACD=180∘ ⇒∠ACB+x=180∘ ⇒∠ACB=(180∘−x)− (ii) From (i) and (ii), we have ⇒∠ABC=(180∘−x) Now, In △ABC ∠ABC+∠ACB+∠BAC=180∘ ⇒(180∘−x)+(180∘−x)+∠BAC=180∘ ⇒∠BAC=180∘−360∘+2x ⇒∠BAC=2x−180∘ ∴ The value of ∠BAC is 2x−180∘ .