Question

determining central and inscribed angles in circles

in circle o, m∠wzj = 19.85°
use the interactive diagram to determine mwj and m∠woj

the m∠woj is degrees.
reason:

Explanation:

Step1: Use the arc - angle relationship

The measure of an inscribed angle is half the measure of its intercepted arc. Here, \(\angle WZJ\) is an inscribed angle and \(WJ\) is its intercepted arc.
Since \(m\angle WZJ = 19.85^{\circ}\), by the inscribed - angle theorem \(m\overset{\frown}{WJ}=2\times m\angle WZJ\).

$$m\overset{\frown}{WJ}=2\times19.85^{\circ}$$

$$m\overset{\frown}{WJ}=39.7^{\circ}$$

Step2: Use the central - angle relationship

The measure of a central angle is equal to the measure of its intercepted arc. For central angle \(\angle WOJ\) and arc \(WJ\), since \(m\overset{\frown}{WJ} = 39.7^{\circ}\), then \(m\angle WOJ=m\overset{\frown}{WJ}\)

Answer:

Measure	Reason
\(m\angle WOJ = 39.7^{\circ}\)	Central - angle theorem (\(m\angle WOJ=m\overset{\frown}{WJ}\))