The corners CAB and BAD are adjacent. Find the value of the angle between the perpendicular drawn

The corners CAB and BAD are adjacent. Find the value of the angle between the perpendicular drawn from point A to line CD and the bisector of angle CAB, if ∠ CAB-∠ ВAD = 20 °.

Since the sum of adjacent angles is 1800, then ∠CAB + ∠ВAD = 180.

By the condition ∠CAB – ∠ВAD = 20 °.

Add the two equations and find ∠ CAB.

∠ CAB + ∠ CAB = 180 + 20.

2 * ∠ CAB = 20.

∠ CAB = 100.

Since AM, by condition, is the bisector of the angle CAB, then ∠ CAC = ∠ CAB = ∠ CAB / 2 = 100/2 = 50.

Then the sought angle ∠ KAM = ∠ CAM – ∠ CAK = 90 – 50 = 40.

Answer: ∠ KAM = 40.