Answer:
Step-by-step explanation:
The interior angle marked 5y is the supplement of the adjacent exterior angle marked 45°.
5y + 45° = 180°
5y = 135° . . . . . . . . subtract 45
y = 27° . . . . . . . . divide by 5
__
The sum of the interior angles of a pentagon is (5-2)(180°) = 540°.
90° +5y +z +82° +135° = 540°
Using y=27°, we can subtract 442° from both sides to get ...
z = 98°
_____
Additional comment
You might recognize that the downward-sloping diagonal sides of the figure are parallel, so z and 82° are consecutive interior angles, hence supplementary. This fact means you don't have to be concerned with the other three angles in the figure to find the value of z: 180° -82° = 98°.
