Question

In the above figure ∠ AOB =80°. What dose ∠ ACB equal?A. 40 B. 80 C. 10D. 160

Answer 1

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

The answer is 40°

Answer 2

Answer:

Find out the what does  ∠ ACB equal .

To prove

As given

∠ AOB =80°

By using the relationship between the inscribed angle and central angle.

$Inscribed\ angle = \frac{1\times central\ angle}{2}$

Here

Inscribed angle = ∠ACB

Central angle = ∠AOB = 80°

$\angle ACB = \frac{80}{2}$

∠ACB  = 40°

Option (A) is correct .