Question

In isosceles triangle $ABC$, the measure of angle $A$ is ${80}^o$. If another angle of the triangle measures $x^o$, where $x\ne 80$, what is one smaller value of $x$?

Answer 1

In isosceles triangle, two angles are equal and sum of three angles is $180$.

Given that one of the vertex angle is $80$.

Case $1:$ angle $80$ is one of the two equal angles, then $x=180-80-80=20$.

Case $2:$ angle $80$ is not one of the two equal angles, then $x=\frac{(180-80)}{2}=\frac{100}{2}=50$.

So, the two possible angles are $20$ and $50$.
the smaller value is $20$