Given:
In circle O, m∠R = 30.8°.
To find:
The m∠NOQ
Solution:
Central angle theorem: According to this theorem, the central angle is always twice of subtended angle on the same arc.
Angle NOQ and angle NRQ are on the same arc but ∠NOQ is the central angle and ∠NRQ is the subtended angle on the arc NQ.
Using central angle theorem, we get
[tex]m\angle NOQ=2\times m\angle NRQ[/tex]
[tex]m\angle NOQ=2\times m\angle R[/tex]
[tex]m\angle NOQ=2\times 30.8^\circ[/tex]
[tex]m\angle NOQ=61.6^\circ[/tex]
Therefore, [tex]m\angle NOQ=61.6^\circ[/tex].
