SOLUTION: http://postimg.org/image/6omaybq21/ I tried approximating angle measures and ended up getting the right answer, J. However, I feel this is incorrect and would like to know a bet

Algebra ->  Circles -> SOLUTION: http://postimg.org/image/6omaybq21/ I tried approximating angle measures and ended up getting the right answer, J. However, I feel this is incorrect and would like to know a bet      Log On


   



Question 987868: http://postimg.org/image/6omaybq21/
I tried approximating angle measures and ended up getting the right answer, J. However, I feel this is incorrect and would like to know a better way of solving it.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

use:
Inscribed angle theorem.
The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.
so, angle MCN=45°
now, in right angle triangle MNO, if you connect M and+N, the other two angles will be 45° each
then we have triangle CMN where one angle is MCN=45° and other two angles are CMO+%2B45 and CNO%2B45
if so, then the sum of all angles in a triangle CMN is:
+%28CMO%2B45%29+%2B+%28CNO%2B45%29%2B45=180
+CMO%2B45+%2B+CNO%2B45%2B45=180
+CMO%2B+CNO%2B135=180
CMO%2B+CNO=180-135
CMO%2B+CNO=45°
so, your answer is: J. 45°