x =
a) 32
b) 64
c) 82

The answer should be 32. Try out this formula:
1/2[(114 + x) - (50 + x)]
Try substituting 32 in for the x
1/2[(114 + 32) - (50 + 32)]
114 + 32 = 146
50 + 32 = 82
146 - 82 = 64
What's half of 64? (Hence the 1/2 in the formula)
32.
So you should get what you substituted in for x on the other two numbers, which we did. : )
Here is why 64 would not work. -
1/2[(114 + 64) - (50 + 64)]
114 + 64 = 178
50 + 64 = 114
178 - 114 = 64
We would still have to divide it by 2, so the answer is obviously not 64.
I hope this helps!
Answer: a) 32°
Step-by-step explanation:
x = far arc - near arc / 2
far arc = x + 114°
near arc = x + 50°
x = (x + 114°) - (x+ 50°) / 2
x = x + 114° -x - 50° / 2
x= 114° - 50° / 2
x = 64 / 2
x= 32°