Answer:
z = 110°
w = 80°
x = 0°
Step-by-step explanation:
Start with the 100° angle. The vertical angle is also 100°. Supplementary angles add up to 180°, so the angle beside it is 80°.
External angles equal the sum of the opposite internal angles, so the other internal angle is 50°. The angle supplementary to that is 130°.
The angle supplementary to the 120° angle is 60°. Angles of a quadrilateral add up to 360°, so the remaining angle is 70°. This angle is supplementary to z, so z is 110°.
TUVW is a parallelogram (a quadrilateral where opposite angles are congruent). Therefore, angle W is 80°. (You could also use the fact that angles of a quadrilateral add up to 360°.)
Angles of a quadrilateral add up to 360°, so:
90 + 84 + 2x + 118 + 2x + 68 = 360
4x + 360 = 360
4x = 0
x = 0
