Question

if the angles of a triangle are in the ratio of 5 : 6 :9 then what is the difference between the greatest and smallest angle

Answer 1

let the angles be 5x,6x,9x



greatest angle = 9x
smallest angle = 5x
difference = 9x-5x = 4x



now,
5x +6x+9x=180°
20x = 180°
4x = 180/5°=36 °




difference is 36°




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Answer 2

let the 1st angle be 5x
let the 2nd angle be 6x
let the 3rd angle be 9x

5x + 6x + 9x = 180° (angle sum property of triangle)

20x = 180°
x = 180/20
x = 9

1st angle = 5x = 5 × 9 = 45°

2nd angle = 6x = 6 × 9 = 54°

3rd angle = 9x = 9 × 9 = 81°

to find the difference
largest angle - smallest angle

81° - 45°
= 36°

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