Question

In $∆ABC,AB=AC$ and $\angle A=100°$, find $\angle B$ and $\angle C.$

Answer 1

Step 1. Given Data.

A triangle with $AB=AC$

Measure of $\angle A=100°$

Step 2. Calculating $\angle B$ and $\angle C.$

We know, $AB=AC$

Theorem: Angles opposite to equal sides are equal.

Therefore, $\angle B=\angle C$

In $∆ABC$, Since the sum of all angles in a triangle is equal to $180°$

$\angle A+\angle B+\angle C=180°$

$$\begin{gathered} \Rightarrow 100°+\angle B+\angle C=180° \\ \Rightarrow 100°+\angle B+\angle B=180°[\angle B=\angle C] \\ \Rightarrow 100°+2\angle B=180° \\ \Rightarrow 2\angle B=180°-100° \\ \Rightarrow 2\angle B=80° \\ \Rightarrow \angle B=\frac{80}{2}=40° \end{gathered}$$

Therefore, $\angle B=\angle C=40°$.