Respuesta :

Hrishii

Answer:

x = 40°

Step-by-step explanation:

In circle with center O.

  • [tex]\angle AOB[/tex] is central angle.

  • [tex]m\angle AOB= 80\degree[/tex] (Given)

  • [tex]m\widehat{(AB)} =m\angle AOB[/tex] (By central angle theorem)

  • [tex]\implies m\widehat{(AB)} =80\degree[/tex]

  • [tex] \angle ACB[/tex] is inscribed angle and [tex]\widehat{(AB)}[/tex] is intercepted by it.

  • [tex]\implies m\angle ACB=\frac{1}{2}\times m\widehat{(AB)}[/tex] (By inscribed angle theorem)

  • [tex]\implies x=\frac{1}{2}\times 80\degree[/tex]

  • [tex]\implies \huge\purple{ x=40\degree}[/tex]