Question

in the given figure ab is perpendicular to BC and AD is the bisector of angle A if angle abc is equal to 70 degree and ACB is equal to 20 degree find angle MAN

Answer 1

Here's the answer to your question.

Answer 2

Answer:

∠MAN=25°

Step-by-step explanation:

Since, AN is the bisector of ∠ABC, therefore, ∠BAN=∠NAC.

Let  ∠BAN=∠NAC= x

then from ΔABC, we have

∠ABC+∠BAC+∠ACB=180°(Angle sum property)

⇒70°+(∠BAN+∠MAC)+20°=180°

⇒2x=90°

⇒x=45°

Now, in triangle ABM, using the exterior angle property,

∠AMC=∠ABM+∠BAM

⇒90°=70°+∠BAM

⇒∠BAM=20°

Now,  ∠MAN=x-∠BAM

⇒∠MAN=45°-20°

⇒∠MAN=25°