IKMC 2027 - Grades 7-8 - Self-study SET 4 - Thematic Batch 3 Question 27

Question 27

In triangle ABC, D lies on AC with $DC=AB$. Points M and N are the midpoints of AD and BC respectively. Given $\angle NMC=\alpha$, express $\angle BAC$ in terms of $\alpha$.

Question illustration

$2\alpha$
$90^\circ-\alpha$
$45^\circ+\alpha$
$90^\circ-\frac\alpha2$
$60^\circ$