Question 439418
The bisector of a vertical angle on isosceles triangle is a perpendicular bisector. Let x degree the vertical angel ( The angel opposite the base)

The bisector divide isosceles triangle in two equal right triangles, solving one of them we have:

{{{sin(x/2)=4/13}}} or sin^-1(4/13)=18, therefore x/2=18 => x=36 degree.

Answer:The vertical angel is approximately 36 degree.