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

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Solution

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 $20$

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