In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, then ∠MAN = ?

Question

In the given figure, AM ⊥ BC and AN is the bisector of ∠ A. If ∠ ABC = 70° and ∠ ACB = 20°, then ∠ MAN = ?

Philoid · Accepted Answer

In triangle ABC,

∠B = 70^o

∠C = 20^o

So, ∠A = 180^o – 70^o – 20^o = 90^o

According to question, AN is bisector of ∠A

So, ∠BAN = 45^o

Now, in triangle BAM,

∠B = 70^o

∠M = 90^o

∠BAM = 180^o – 70^o – 90^o = 20^o

Now, ∠MAN = ∠BAN – ∠BAM

= 45^o – 20^o

= 25^o