An exterior angle of a triangle measures 110° and it's it's interior opposite angles are in ratio 2:3 find the measurements of these angles

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Solution

According to property of triangle, measure of exterior angle of a triangle is the sum of other two non adjecent angles of triangle.

so here the sum of 2 given angles must measure up to 110°.

Given that the two interior opposite angles are in the ratio 2:3.

so let X be the common multiple

So 2x+3x= 110
5x=110

X=110/5
=22

So 1st angle is 22×2=44 degree

and 2nd is 22×3=66 degree

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