Question

find the smallest angle of this pentagon x, x-15, x-50, x-30, x-40

Answer 1

Cannot be answered with the information given.
e.g. let x = 60
then you have sides of 60, 45, 10, 30, and 20
Use a ruler and a compass and a scale factor of 1/10,
that is, sides of 6, 4.5, 1, 3, and 2 inches (or cm or..)
construct such a pentagon.
(I actually cut some bamboo skewers to those lengths and formed a pentagon
I was able to "squish" the shape and change the angles.)
Try it.

There is no unique answer to the question.


For some interesting problems relating to this topic, try this question:
Show that a quadrilateral of sides 3, 4, 5, and 6 has the largest area when opposite angles are supplementary.