Dear Sir, In triangle ABC, angle B is greater than angle C If AM is the bisector of angle - Maths - Triangles

Question

Dear Sir,
In triangle ABC, angle B is greater than angle C If AM is the
bisector of angle BAC and AN is perpendicular to BC, prove that
angle MAN = 1/2 (angle B - angle C)
Please help me
Rgds
Meherchand

Priyanka Kedia · Accepted Answer

$I n t r i a n g l e A B C, A M i s t h e b i \sec t o r o f ∠ B A C, s o, ∠ B A M = ∠ C A M = x S i n c e s u m o f a n g l e s o f a t r i a n g l e = 180^{0} T h e r e f o r e, ∠ A + ∠ B + ∠ C = 180^{0} \Rightarrow (∠ B A M + ∠ C A M) + ∠ B + ∠ C = 180^{0} \Rightarrow (x + x) + ∠ B + ∠ C = 180^{0} \Rightarrow x = 90^{0} - (\frac{∠ B + ∠ C}{2}) N o w, i n r i g h t t r i a n g l e C A N, ∠ C A N + ∠ C = 90^{0} \Rightarrow (x + ∠ M A N) + ∠ C = 90^{0} \Rightarrow ∠ M A N = 90^{0} - ∠ C - x \Rightarrow ∠ M A N = 90^{0} - ∠ C - [90^{0} - (\frac{∠ B + ∠ C}{2})] \Rightarrow ∠ M A N = \frac{∠ B - ∠ C}{2} H e n c e p r o v e d .$

Dear Sir, In triangle ABC, angle B is greater than angle C. If AM is the bisector of angle BAC and AN is perpendicular to BC, prove that angle MAN = 1/2 (angle B - angle C). Please help me. Rgds Meherchand

Dear Sir,

In triangle ABC, angle B is greater than angle C. If AM is the bisector of angle BAC and AN is perpendicular to BC, prove that angle MAN = 1/2 (angle B - angle C).

Please help me.

Rgds

Meherchand