Question

In triangle ABC , AM is perpendicular to BC and AN is the bisector of angle A. Find the measure of angle MAN, when angle B = 70 degree and angle C =35

Answer 1

$\boxed{\boxed{\huge{Question:-}}}$

➡In triangle ABC , AM is perpendicular to BC and AN is the bisector of angle A. Find the measure of angle MAN, when angle B = 70 degree and angle C =35.

$\boxed{\boxed{\huge{Answer:-}}}$

$\: Angle \: MAN \: = \frac{35}{2} = 17.5 \: degree$

$\boxed{\boxed{\huge{Solution:-}}}$

Let, the angle A be 2x. {An is bisector of angle A. }

➡∠BAN = ∠NAC = x

In ΔABC,

=>∠B + ∠C + ∠A = 180°

=>65 + 30 + ∠A = 180°

=>∠A = 85°

$so \: . \: x = \frac{8}{5}$

In, ΔABN ,∠ANC is exterior angle of ΔABN,

➡x + 65 = ∠ANC

➡85/2 + 56 = ∠ANC

➡∠ANC = 215/2

➡∠MNA = 180 - 215/2 = 143/2

∴∠MNA =143/2

In ΔAMN,

➡143/2 + 90 + ∠MAN = 180°

➡∠MAN = 90 - 143/2

➡∠MAN = 35/2

∴∠MAN =17.5 °

.................Solved✔✔✔✔✔✔✔✔

Answer 2

Let the angle  A  be  2x. As AN is bisector of  angle  A , Therefore,

∠BAN = ∠NAC = x

in ΔABC,

∠B  + ∠C + ∠A = 180°

65 + 30 + ∠A = 180°

∠A = 85°

Hence, x = 85/2

in ΔABN, ∠ANC is exterior angle of ΔABN,

x + 65  = ∠ANC

85/2 + 56 = ∠ANC

∠ANC = 215/2

∴∠MNA = 180  - 215/2 = 143/2

in ΔAMN,

143/2 + 90 + ∠MAN = 180°

∠MAN = 90 - 143/2

∠MAN = 35/2