angle aob = 80 degrees. what does angle acb equal? ( figure is a circle)?

Question

a- 10 degrees
b- 40 degrees
c- 80 degrees
d- 160 degrees

Answer 1

Very difficult to guess without seeing the drawing.

I am going to suppose the following:

a, b and c are points on the circumference.
o is the centre of the circle.

If that is the case, then angle aob = 80 degrees means that the arc "ab" measures 80 degrees also.
A "length" on a circumference is measured in fractions of the total circumference and the total circumference is 360 degrees.

Angles at the centre = length of subtended arc.
angle aob = 80 means arc "ab" = 80.

If c is on the other side of the circle (outside the shorter arc "ab") then it is an inscribed angle.
Any inscribed angle is worth exactly half of the arc it subtends.

If angle acb subtends the same arc "ab" = 80 degrees, then the angle is worth half of that. acb = 40 degrees.

And it does not matter where c is located, as long as it is on the circumference (an inscribed angle) and outside the short portion of "ab" (c subtends 80 degrees), it will always be an angle of 40 degrees.

If c is located between a and b (inside the 80 degree arc), then it subtends the rest of the circumference (360-80 = 280) and the angle is worth half of that = 140 degrees.

Answer 2

If C is on the circle somewhere, and O is the center, then angle ACB is inscribed, which makes its measure be half of that of angle AOB, which is a central angle. So find half of 80 degrees.