Ok, so
We know that two circles are congruent. This makes that the triangles there, are cogruent.
Let me draw the situation here below:
If both triangles are congruent, that means that their sides and angles are equal.
Now if we notice, we realize that side DG and side NM will be equal.
So, DG = NM
Which is the same that
14t - 26 = 5t + 1
If we solve the equation for t:
14t - 5t = 26 + 1
9t = 27
And t = 3
Now, we want to find NM measure.
And we just have to replace t=3 in the expression 5t+1
This will be 5(3) + 1, which is 16.
Therefore, NM measures 16.