Given:
A circle with center O.
[tex]m\angle MOP=45^\circ, m\angle PON=85^\circ[/tex].
To find:
The measure of arc MN.
Solution:
We know that,
[tex]m\angle MON=m\angle MOP+m\angle PON[/tex]
[tex]m\angle MON=45^\circ+85^\circ[/tex]
[tex]m\angle MON=130^\circ[/tex]
The central angles in equal to the measure of the corresponding arc.
[tex]Arc(MN)=m\angle MON[/tex]
[tex]Arc(MN)=130^\circ[/tex]
Therefore, the measure of arc MN is 130 degrees.
