Question

In $\mathrm{\Delta }\mathrm{ABC},\mathrm{BC}=\mathrm{AB}\mathrm{and}\angle \mathrm{B}=80°$. Then $\angle \mathrm{A}$ is equal to

• A. $80°$
• B. $40°$
• C. $50°$
• D. $100°$

Answer 1

The correct option is C

$50°$

The explanation for the correct answer.

Given: $\angle \mathrm{B}=80°\mathrm{and}\mathrm{AB}=\mathrm{BC}\mathrm{in}∆\mathrm{ABC}$

Here $\mathrm{AB}=\mathrm{BC}$

Therefore, triangle ABC is an isosceles triangle.

$$\begin{gathered} \mathrm{Now}\mathrm{in}∆\mathrm{ABC} \\ \angle \mathrm{A}=\angle \mathrm{C}(\because ∆\mathrm{ABC}\mathrm{is}\mathrm{an}\mathrm{isosceles}\mathrm{triangle}) \\ \because \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°\mathbf{}(\mathrm{Angle}\mathrm{sum}\mathrm{property}\mathrm{of}\mathrm{triangle}) \\ \Rightarrow \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}2\angle \mathrm{C}+\angle \mathrm{B}=180°(\because \angle \mathrm{A}=\angle \mathrm{C}) \\ \Rightarrow 2\angle \mathrm{C}+80=180 \\ \Rightarrow 2\angle \mathrm{C}=180-80 \\ \Rightarrow 2\angle \mathrm{C}=100 \\ \Rightarrow \angle \mathrm{C}=\frac{100}{2} \\ \Rightarrow \angle \mathrm{C}=50° \end{gathered}$$

Hence option (C) is correct.