Question

In acute triangle ABC, we have ∠CAB=34∘. E is the foot of the perpendicular from B to AC. A point H is on BE is chosen, and X is the foot of the perpendicular from H to AB. What is the measure (in degrees) of ∠EHX?

Answer 1

Drop an altitude from X to meet AC at point Y.

Then XY ║ BE

∠AXH is 90°, so ∠YXH is 34°.
So, since the angles at Y and E are all 90°, ∠EHX = 180-34 = 146°