Question

An isosceles triangle has base angles equal. If its vertex angle is ${80}^o$, then find its base angles.

Answer 1

According to the angle sum property, the sum of all the angles of a triangle is ${180}^o$

Let the angles of a triangle be $a,b,c$.

Let the base angles of isosceles triangle are $b,c$. …(I)

According to questions $b=c$.

Now , $a+b+c={180}^o$ …(angle sum property)

$\Rightarrow {80}^o+b+c={180}^o$

$\Rightarrow {80}^o+b+b={180}^o$ …(from I)

$\Rightarrow 2b={180}^o-{80}^o$

$\Rightarrow b={50}^o$

Hence, The base angles are ${50}^o$ each.