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Question

In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, then ∠MAN = ?
(a) 20°
(b) 25°
(c) 15°
(d) 30°

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Solution

(b) 25°

In ABC, we have:
A+B+C=180° Sum of the angles of a triangleA+70°+20°=180°A=90°12A=45°BAN=45°
In ABM, we have:
ABM+AMB+BAM=180° Sum of the angles of a triangle70°+90°+BAM=180°BAM=20°MAN=BAN-BAMMAN=45°-20°MAN=25°

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