Question

find the measure of the arc. mbc = ?°

Explanation:

Step1: Recall circle - arc measure relation

The sum of central angles in a circle is 360°.

Step2: Identify relevant central angles

We see a right - angle (90°) and a 140° angle in the inner circle. Let the central angle corresponding to arc $\widehat{BC}$ be $x$.

Step3: Calculate the central angle for arc $\widehat{BC}$

We know that the non - overlapping central angles around a point sum to 360°. The central angle for arc $\widehat{BC}$ can be found by considering the fact that the sum of the angles in the inner circle and the outer - circle relationships. Since the angles in the inner circle are part of the whole - circle angle structure, and we assume the circle is divided into non - overlapping sectors. The central angle corresponding to arc $\widehat{BC}$ is equal to the sum of the right - angle and the 140° angle. So $x=90 + 140$.

Step4: Compute the value

$x = 230$.

Answer:

230