Question 1059245
Ratio; Isosceles;  the description should be clear.


VERTEX to BASE,
8:5


How many base-angles?  Two, because isosceles triangle will have two angles of equal measure and one angle of different measure.


What else do you know? 
Sum of the interior angle measures is 180 degrees.


--
Are you still stuck?
If so, maybe you need to say the vertex angle is some product with a factor of some variable, p.
Vertex angle measure is some 8p and you expect ratio of vertex to base is {{{(8p)/(5p)}}};
and you also expect  {{{8p+5p+5p=180}}}.
-
-
You are only about two or three simple steps away from finding measure of the vertex angle.