In triangle ABC, angle A = 74, heights AD and CE intersect at point O, find angle DOE.

1. The AВD triangle is rectangular, since the height of the ВD forms an angle equal to 90 ° with its side ABP.

2. We calculate the degree measure ∠AВD, taking into account that the sum of all angles of the triangle, according to its properties, is 180 °:

∠AВD = 180 ° – 90 ° – 74 ° = 16 °.

3. We calculate the value ∠BOE, taking into account that the triangle BOE is rectangular, since the height of CE forms an angle equal to 90 ° with its side BE:

∠BOE = 180 ° – 90 ° – 16 ° = 74 °.

4. Calculate the degree measure of the required ∠DOE, taking into account that ∠DOE and ∠BOE are adjacent, and their sum is 180 °:

∠DOE = 180 ° – 74 ° = 106 °.

Answer: ∠DOE = 106 °.