In the diagram, m∠coe = 55°. if m∠2 = 2x and m∠3 = x+10, what is the measure of angle 2?

15

30

45

60

So here is how we are going to get the measure of angle 2. 
Since given that angle COE measures 55°, we will equate m∠2 = 2x and m∠3 = x+10 with 55. So, 55 = 2x + x + 10
55 = 3x + 10
55-10 = 3x
45 = 3x << divide both sides by 3 and the result is 
15 = x
So now that we know x, we can now solve for angle 2.
m∠2 = 2x
m∠2 = 2(15)
m∠2 = 30°
I hope that this is the answer that you are looking for.