In triangle ABC, the angles of which are ∠B = 40∘ and ∠C = 80∘, the height CH is drawn. Find the ACH angle (in degrees).

Find the value of the angle A in triangle ABC. The sum of the angles of any triangle is 180 degrees, so:
A + B + C = 180
A + 40 + 80 = 180
A = 180 – 80 – 40 = 60 degrees.
In triangle ACH, the angle H is 90 degrees because CH is the height. The sum of the angles of any triangle is 180 degrees, so:
A + C + H = 180
60 + C + 90 = 180
C = 180 – 60 – 90 = 30 degrees.
Answer: 30 degrees.