Question

In triangle ABC, if $BC=AC$ and $\angle B={40}^{\circ }$. Then $\angle C$ is equal to

___ degrees.

Answer 1

In a triangle, if two sides are equal then it is an isosceles triangle. The angles opposite to the two equal sides are also equal.

Therefore, $\angle A=\angle B$

Since sum of all the angles in a triangle $={180}^{\circ }$

$\Rightarrow$ $\angle A+\angle B+\angle C={180}^{\circ }$

$\Rightarrow$ $2\times {40}^{\circ }+\angle C={180}^{\circ }$ ($\angle A=\angle B$)

$\Rightarrow$ $\angle C$$={180}^{\circ }-2\times {40}^{\circ }$

$\Rightarrow$ $\angle C$$={100}^{\circ }$