Question

Three angles of tringle 4:5:6, then find the ratio between biggest and smallest angle?

Answer 1

1st : 2nd : 3rd : sum
4 : 5 : 6 : 15
: 180 <-- (sum of angles of triangle)
1st angle = 180×4/15 =48°
2nd angle = 180×5/15 =60°
3rd angle = 180×7/15 = 72°
so you can see the smallest angle is 48° and the biggest one is 72°
so the ratio between them is 48/72 = 2/3
2 : 3

Answer 2

Let the angles of triangle be 4x,5x,6x
4x+5x+6x=180
15x=180
x=180/15
x=12.
4*12=48°(Smallest angle)
5*12=60°
6*12=72°(Biggest angle)
Ratio=Biggest angle:Smallest angle
        =72:48
        =2:3