In Fig. 9.37, AM ⊥ BC and AN is the bisector of ∠A. If ∠B =65° and ∠C =33°, find ∠MAN.

Given,

AM perpendicular to BC

AN is bisector of A

Therefore, NAC = NAB

In

A + B + C = 180o

A + 65o + 33o = 180o

A = 180o – 98o

= 82o

NAC = NAB = 41o (Therefore, AN is bisector of A)

In

AMB + MAB + ABM = 180o

90o + MAB + 65o = 180o

MAB + 155o = 1800

MAB = 25o

Therefore,

MAB + MAN = BAN

25o + MAN = 41o

MAN = 41o – 25o

= 16o

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