The missing variable x is: x = 7
The angle 1 is: ∠1 = 96°
How to find the missing angle?
We are given the angles:
m∠F.KH = (5x + 5)°
m∠KHF = (13x - 7)°
m∠HF.K = (6x + 14)°
Sum of angles in a triangle is 180 degrees. Thus:
(5x + 5)° + (13x - 7)° + (6x + 14)° = 180
24x + 12 = 180
24x = 180 - 12
24x = 168
x = 168/24
x = 7
m∠KHF = (13(7) - 7)°
m∠KHF = 84°
∠1 = 180 - 84
∠1 = 96°