IKMC 2017 - Grades 9-10 - Self-study Question 30

Question 30

D is on side AC of triangle ABC with $DC=AB$. M and N are the midpoints of AD and BC. If $\angle NMC=\alpha$, what does $\angle BAC$ always equal?

Question illustration

$2\alpha$
$90^\circ-\alpha$
$45^\circ+\alpha$
$90^\circ-\alpha/2$
$60^\circ$