geometry!

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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)?

  • geometry! -

    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

  • geometry! -

    85

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