Question

If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then what is the degree measure of angleEOC?

Answer 1

Diagonals of regular pentagon trisect all the interior anglesSo, angle ABO will be 1/3 times interior angle ABCso, angle ABO = 36 similarly angle BAO = 36
so angle AOB will be 180 -36-36(because angle in a triangle sum upto 180)
and since EOC is vertical to AOBEOC = AOB