The total of the interior angles of any polygon is (n – 2) • 180o where n is the number of sides.
The total of the interior angles of this (and every) pentagon is 540o so set up the addition.
z + 2z + 117 + 64 + (2z –6) = 540
5z + 175 = 540
5z = 540 – 175
z = 73o
.
