What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio \(3:5:7\)?
+9519 Note that the exterior angles of any convex polygon always add up to 360 degrees.
Since an interior angle and its corresponding exterior angle always add up to 180 degrees, a larger exterior angle means a smaller interior angle. So we are actually looking for the largest exterior angle.
Using the ratio, we calculate that the largest exterior angle is \(360^\circ \times \dfrac{7}{3 + 5 + 7} = 168^\circ\). You can subtract that from 180 degrees to find the smallest interior angle.
This is one step away from the answer. Please continue on your own, but I hope you have an idea of what I explained, because that would be useful if you are to solve a similar problem entirely on your own.
