Question

please can anyone solve this

Answer 1

noangle ( ABC+BAC+ACB)=180°

=>65°+BAC+30°=180°

=>angle BAC=180°-65°-30°

=>BAC=85°

in the AMC

angle MAN=NAC

angle MAC+AMC+ACM=180°

MAN+NAC+90°+30°=180°

2MAN=180°-90°-30°

2MAN=60°

angle MAN=60°/2=30°

hope it helps u.......

Answer 2

in triangle ABC

∠A+65+30=180 {you know why , do i need to tell you?}

after solving it

we get ∠ A=85

thus half of ∠ A=42.5

now in triangle ANC

42.5+30+∠ANC=180

we get ∠ANC=107.5

180-107.5=∠ANM {corresponding angles}

∠ANM=72.5

in triangle AMN

90+72.5+∠MAN=180

after solving

∠MAN=17.5 (ans.)

let me know if im right k?