Angle NLM is 78 degrees
A way to do this is to find the arc measure of NM and then divide it by 2 to find the angle of NLM
So first subtract
360-110=250
To find the remaining amount of the arc measures. Which is 250 degrees
Next set arc measures NM and ML together to 250 to find what x equals.
14x+16+9x+4=250
Combine like terms
23x+20=250
Subtract 20 from both sides
23x=230
Divide 23 from both sides
x=10.
Then substitute 10 for the equation representing the arc measure of NM.
14(10)+16
140+16
156
The arc measure of NM is 156 degrees
The angle NLM is an inscribed angle. Meaning that it is half of the arc that intersects.
156/2
78
Angle NLM is 78 degrees
