In triangle ABC, angle A is 56 °, angles B and C are sharp, heights B D and CE intersect at point O. Find angle DOE.

After the heights BD and CE were drawn in the triangle ABC, we have a quadrilateral AEOD. There are three known angles in this quadrangle. <A = 56 (by condition), <E = 90, <D = 90 (because BD and CE are heights). The sum of the angles of the quadrilateral is 360 degrees, because the sum of the angles of any polygon is 180 (n – 2), where n is the number of sides of the polygon. We have n = 4, 180 (n – 2) = 180 (4 – 2) = 180 * 2 = 360.

<O = 360 – (<A + <E + <D);

<O = 360 – (56 + 90 + 90) = 360 – 236 = 124.

Answer. 124 degrees.