Question

If in$∆ABC,AB=ACand\angle A=100°$, then find $\angle B$ and $\angle C$.

Answer 1

Step 1: Given data

$In△ABC,\angle A=100°andAB=AC$

$∆ABC$ is an isosceles triangle as two sides are equal.

Therefore,$\angle B=\angle C$ [Angles opposite to equal sides are equal]

Step 2: Finding the measure of $\angle B$ and $\angle C$

$$\begin{gathered} In△ABC, \\ \angle A+\angle B+\angle C=180°(anglesumpropertyof∆) \\ \Rightarrow 100°+2\angle B=180° \\ \Rightarrow \angle B=40° \\ \Rightarrow \angle C=40° \end{gathered}$$

Hence,angles are $\angle B=\angle C=40°$