SOLUTION: try to draw or picture this in your head. there is a circle and 4 points going around it in order M, N, O, P. and point Q intersects lines MO and PN. I am given that angle MPN equa

Algebra ->  Circles -> SOLUTION: try to draw or picture this in your head. there is a circle and 4 points going around it in order M, N, O, P. and point Q intersects lines MO and PN. I am given that angle MPN equa      Log On


   

Question 387197: try to draw or picture this in your head. there is a circle and 4 points going around it in order M, N, O, P. and point Q intersects lines MO and PN. I am given that angle MPN equals 42° and that arc MP equals 100°. I need to find the measure of angle MON and I dont know what to do
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


You don't even need to know the measure of arc PM.  All you need to notice
 
is that inscribed angle MPN and inscribed angle MON subtend the same arc MN.

Since the measure of an inscribed angle is 1/2 of its subtended arc,

both angles MPN and MON have measure of 1/2 of the measure or arc

MN which they subtend.  So they have equal measure.  Therefore the measure 

of angle MON is also 42°.  It didn't require any calculations at all. 



Edwin