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Question

If the exterior angles of a triangle are in the ratio 4:5:6, find the ratio of the angles of the triangle.

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Solution

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 =18096=84

Second Interior angle of the triangle =180120=60

Third Interior of the triangle =180144=36

Ratio of the angles of the triangle =84:60:36=7:5:3


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