If the exterior angles of a triangle are in the ratio 4:5:6, find the ratio of the angles of the triangle.
Let the angles are 4x,5x and 6x
Sum of exterior angle of a triangle =360∘
4x+5x+6x=360∘
⇒15x=360∘
⇒x=24∘
First Exterior angle =4(24)=96∘
Second Exterior angle =5(24)=120∘
third extreior angle =6(24)=144∘
Then, First interior angle of the triangle =180−96=84∘
Second Interior angle of the triangle =180−120=60∘
Third Interior of the triangle =180−144=36∘
Ratio of the angles of the triangle =84:60:36=7:5:3