Question

apply: circle problem #2
point o is the centre of the circle.
what is the value of $\angle x^\circ$?

Explanation:

Step1: Recall the central angle theorem

The central angle theorem states that the measure of a central angle is twice the measure of the inscribed angle subtended by the same arc.

Step2: Identify the angles

The inscribed angle at point I is \(22^\circ\), and the central angle \(\angle x\) subtends the same arc as the inscribed angle.

Step3: Calculate the central angle

Using the central angle theorem, we multiply the inscribed angle by 2. So, \(x = 2\times22^\circ\)
\(x = 44^\circ\)

Answer:

\(44\)