Answer:
238°
Step-by-step explanation:
In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.
So, the angle "21x - 2" and the angle "38x + 5" add up to 180.
So, we can write an equation and solve for x first:
[tex]21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3[/tex]
x = 3
Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:
Angle A = 38x + 5 = 38(3) + 5 = 119
Thus, Arc FGH = 2 * 119 = 238°
