Question

In a ∆ABC, if AB = AC and ∠A = 70°, find ∠B and ∠C.

Answer 1

$$\begin{gathered} ∆\mathrm{ABC}\mathrm{is}\mathrm{an}\mathrm{isosceles}\mathrm{triangle},\mathrm{i}.\mathrm{e}.\mathit{,}\mathrm{AB}=\mathrm{AC}. \\ \therefore \angle \mathrm{ABC}=\angle \mathrm{ACB} \\ \mathrm{In}∆\mathrm{ABC},\mathrm{let}\angle \mathrm{B}=\angle \mathrm{C}=\mathrm{x} \\ \mathrm{Now},\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow 70+\mathrm{x}+\mathrm{x}=180 \\ \Rightarrow 2\mathrm{x}=110 \\ \Rightarrow \mathrm{x}=55° \\ \therefore \angle \mathrm{B}=\angle \mathrm{C}=55° \end{gathered}$$