posted by John .
In acute triangle ABC, we have \angle CAB = 34 ^\circ . 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 \angle of EHX?
very simple, look at quad AXHE
you already have 2 90° angles and a third angle of 34°
all 4 must add up to 360, so
angle EHX = 360 - 90 -90 -34 = 146°