Answer:
x = 121 degrees
y = 59 degrees
w = 59 degrees
z = 53 degrees
v = 121 degrees
Explanation:
31 + 90 + w = 180 ==> these three angles are in the top left triangle.
Triangles add up to 180 degrees
121 + w = 180 ==> solve for w
w = 59 degrees
y = w ==> these angles are opposite adjacent angles; they are congruent
y = 59 degrees ==> Both angles are equal. So both angles are 59 degrees
68 + y + z = 180 ==> triangles add up to 180 degrees
68 + 59 + z = 180 ==> plugin 59 for y
127 + z = 180 ==> solve for z
z = 53 degrees ==> subtract 137 on both sides
w + x = 180 ==> w and x are on a straight line.
Straight lines add up to 180 degrees.
59 + x = 180 ==> plugin 59 for w
x = 121 degrees ==> subtract 59 on both sides
v + y = 180 ==> v and y are also on a straight line.
v + 59 = 180 ==> plugin 59 for y
v = 121 degrees ==> subtract 59 on both sides
x = 121 degrees
y = 59 degrees
w = 59 degrees
z = 53 degrees
v = 121 degrees