ABC is an acute angle triangle with points D and E on BC and AC, respectively such that BE and AD are altitudes. AD and BE intersect at H. If ∠BCA=39∘ and ∠EBA=2∠DAB, what is the measure of ∠ABC (in degrees)?

Answer 1

We have a bunch of right triangles here
BCA=39, so CAD = 51
BEA=90, so EHA = 39
vertical angle DHB is thus 39
HDB = 90, so HBD = 51

Now we know all the angles
A = 51+x
B = 51+2x

so, 39+51+x+51+2x = 180
x = 13

ABC = 26

Answer 2

85