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In triangle ABC we have
angle A + angle B + angle C = 180° (since sum of all angles is 180°)
angle A + 70° + 20° = 180°
angle A = 180° - 90° = 90°
In triangle AMB we have
angle ABM + angle BAM + angle AMB = 180°
70° + 20° + angle AMB = 180°
angle AMB = 180°-90° = 90°
In triangle AMC we have
angle AMC + angle ACM + angle MAC = 180°
90° + 20° + angle MAC = 180°
angle MAC = 180°- 110° = 70°
Now we know that AN is bisector of Angle A .
Angle A = 90°
angle A = angle BAN + angle NAC
so angle BAN = angle NAC = 45° ( since AN is bisecting angle A )
now
Angle BAN = angle BAM + angle MAN
45°= 20° + angle MAN
angle MAN = 45°- 20° = 25°
hence found
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