Question: Is x less than 80 degrees?

"How can we assume that it is the diameter of the circle?"
The diameter is the longest chord in a circle. So, if the radius is 4, and statement 1 says that CB = 8 (i.e., twice the radius), then we can be certain that CB is the diameter of the circle.

"Also nowhere it is written that figure is not drawn to scale."
You might want to look a little more closely :-)

Yes, it's still sufficient. It all comes down to whether we can answer the target question with certainty.

Here, the target question is "Is x less than 80?"

Statement 1 essentially tells us that x = 90. So, our answer to the target question is "No, x is not less than 80."

Since we can answer the target question with certainty, statement 1 is sufficient.

Likewise, IF it were the case that statement 1 told us that x = 70, then the answer to the target question would be "Yes, x is less than 80." Since we could answer the target question with certainty, statement 1 would be sufficient.