In triangle ABC, angle CAB = 26 degrees, angle ACB = 64 degrees. Segment AD is perpendicular

In triangle ABC, angle CAB = 26 degrees, angle ACB = 64 degrees. Segment AD is perpendicular to the plane of triangle ABC. Determine the angle between straight lines BD and BC.

In a given triangle ABC, the sum of two acute angles is 90 ° (26 ° + 64 °). We conclude that triangle ABC is rectangular, angle B = 90 °. AB is perpendicular to BC.
We get:
AB is perpendicular to BC.
AD – perpendicular to the ABC plane (by condition);
BD – oblique;
AB – projection of the inclined BD on the plane.
According to the three perpendicular theorem, we have the following:
The projection AB is perpendicular to the straight line BC, then the inclined BD is perpendicular to the straight line BC.
Answer: the angle between straight lines BD and BC is 90 °.