Answer:
[tex]\angle a=35^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
An isosceles triangle has two equal sides and two equal interior angles
The angles opposite to the equal sides of an isosceles triangle are equal.
[tex]\angle b=\angle c[/tex]
we have
[tex]\angle c=55^o[/tex] -----> given problem
so
[tex]\angle b=55^o[/tex]
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
[tex]\angle b+\angle c+2\angle a=180^o[/tex]
substitute the given values
[tex]55^o+55^o+2\angle a=180^o[/tex]
[tex]110^o+2\angle a=180^o[/tex]
[tex]2\angle a=180^o-110^o[/tex]
[tex]2\angle a=70^o[/tex]
[tex]\angle a=35^o[/tex]
