simple geometry!
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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?

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 = 18034 = 146°
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