Question

Find the measurement of x

Answer 1

Answer:

x = 40°

Step-by-step 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.

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

• $\implies x=\frac{1}{2}\times 80\degree$

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