If the angles of a triangle are in the ratio of 9:11:16, then the difference between the greatest angle and the smallest angle is:

Let the angles of the triangle be 9k, 11k, and 16k.
According to the angle sum property of a triangle, the sum of all internal angles is 180
∘
:

9k+11k+16k=180
∘

36k=180
∘
⟹k=
36
180
∘

​
=5
∘

The greatest angle is 16k and the smallest angle is 9k.
The difference between the greatest and smallest angle is:

Difference=16k−9k=7k
Difference=7×5
∘
=35
∘