Math,geometry

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle ACB = 39^\circ$. Find $\angle PBC$ in degrees.

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  1. How about just typing:
    Point P is on side AC of triangle ABC such that angle APB =angle ABP, and angle ABC - angle ACB = 39°. Find angle PBC in degrees.
    let angle APB = angle ABP = x
    let angle PBC = y, let angle BCP = k

    given:
    x+y - k = 39
    k = x+y-39

    In triangle PBC, the angles add up to 180°
    y + 180-x + k = 180
    y + 180 - x + x+y-39 = 180
    2y = 39
    y = 39/2 = 19.5°

    check my arithmetic

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    Reiny

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