So if the exterior angle is 130°, then the inner angle is 50°.
The total of the inner angles of a triangle is (n-2)180°=180°, so 180°-50°=130°
With the remaining two angles =130° and they are both in the ratio of 2:3, one angle has a measure of 52° and 78°.
Thus the measure of the largest angle is 78°.