Question

If the measure of the arc LN=80° and the measure of arc OP=50°, then m∠M=__

Answer 1

now
\[\angle LCN=80,\angle OCP=50.\]
\[\angle NLC= \angle LNC= \angle x, \angle COP=\angle CPO= \angle y, \angle CLO=\angle COL= \angle CNP=\angle CPN= \angle a\]\[2x +2y+4a=360\]
in triangle LCN
2x+80=180
2x=100
in triangle OPC
2y +50=160
2y=130
solve to get a
then solve for triangle MLN