Question

A wooden plate is shaped as a pentagon. The measure of one angle is 20°. The remaining interior angles are obtuse and of equal measure.
What is the measure of each obtuse angle in the pentagon?

Answer 1

A good way to think about the interior angles of polygons is to say this: imagine I am walking along the edge, then for an n-sided polygon each turn away from the direction I was headed is 360 / n (so that in the end I am headed as I was in the beginning).

For a regular pentagon that's 72 degrees at each turn, the supplementary interior angle is 180 - 72 = 108, and totaling 540 for the 5 vertices.

But this is an irregular pentagon. One angle is 20, so the sum of the remaining 4 is 520, distributed over 4 equal angles.

Answer 2

you can make 2 triangles relative to a single given corner with a pentagon. that means the sum of its interior angles= 360
therefore 360-20=340/4 = 85 deg