In circle P, arc EN=66, angle GPM=89, and GN is the diameter. Find the measure of angle EGN.
The answer is 33º but I'm not sure how you get it.
There is a theorm that says the inscribed angle of a circle arc is 1/2 the arc (or one half the central angle).
http://en.wikipedia.org/wiki/Circle#Inscribed_angles
Theta= 1/2 EN
To find the measure of angle EGN, we can use the properties of inscribed angles in a circle.
From the given information, we know that EN is an arc of circle P and its measure is 66. According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc.
Therefore, we can say that the measure of angle EGN is equal to half the measure of arc EN. So, angle EGN = 1/2 * 66 = 33 degrees.
Hence, the measure of angle EGN is 33 degrees.