Question 575440
The axis altitude (or median) through the vertex splits the vertex angle into two congruent angles and splits the isosceles triangle into two congruent right triangles.
{{{drawing(300,300,-8,8,-3,13,
triangle(-7,0,7,0,0,10.9545),
red(line(0,0,0,10.9554)),
rectangle(0,0,0.5,0.5),
locate(3.5,6.5,13),locate(-4.3,6.5,13),
locate(-3.8,1,7),locate(3.3,1,7),
locate(-0.2,0,D),locate(-0.2,11.7,B),
locate(-8,0.5,A),locate(7.5,0.5,C),
locate(-0.5,-1.5,14), arrow(-0.6,-2,-7,-2), arrow(0.6,-2,7,-2)
)}}}
In each of those right triangles the angle at the isosceles triangle vertex is opposite a side measuring 7 cm, while the hypotenuse measures 13 cm.
{{{sin(ABD)=7/13}}} ---> {{{ABD=32.579^o))) (approximately)
So {{{ABC=2*ABD=2*32.579^o=65.158^o}}}
So to the nearest degree {{{highlight(angleABC=65^o)}}}