Question

Find the measurement of x

Answer 1

x = 40°

Explanation:

In circle with center O.

• 
  `\angle AOB` is central angle.

• 
  `m\angle AOB= 80\degree` (Given)

• 
  `m\widehat{(AB)} =m\angle AOB` (By central angle theorem)

• 
  `\implies m\widehat{(AB)} =80\degree`

• 
  `\angle ACB` is inscribed angle and
  `\widehat{(AB)}` is intercepted by it.

• 
  `\implies m\angle ACB=(1)/(2)* m\widehat{(AB)}` (By inscribed angle theorem)

• 
  `\implies x=(1)/(2)* 80\degree`

• 
  `\implies \huge\purple{ x=40\degree}`