Answer:
a = 20°
b = 160°
c = 125°
u = 110°
v = 70°
w = 110°
x = 70°
y = 110°
z = 110°
Step-by-step explanation:
Theorems
- Vertical Angles Theorem: When two straight lines intersect, the vertical angles are congruent.
- Angles on a straight line: Angles on a straight line sum to 180°.
- Corresponding Angles Postulate: When two parallel lines are cut by a transversal, the corresponding angles are congruent.
- Same-side Exterior Angles: When two parallel lines are cut by a transversal, the same-side exterior angles sum to 180°.
Using the Vertical Angles Theorem:
⇒ a = 20°
Using the Angles on a straight line Theorem:
⇒ 20° + b = 180°
⇒ b = 180° - 20°
⇒ b = 160°
Using the Vertical Angles Theorem:
⇒ c + 35° = b
⇒ c + 35° = 160°
⇒ c = 160° - 35°
⇒ c = 125°
Using the Vertical Angles Theorem:
⇒ u = 110°
⇒ v = 70°
Using the Same-side Exterior Angles Theorem:
⇒ v + w = 180°
⇒ 70° + w = 180°
⇒ w = 180° - 70°
⇒ w = 110°
Using the Corresponding Angles Postulate:
⇒ y = 100°
Using the Vertical Angles Theorem:
⇒ y = z = 110°
Using the Angles on a straight line Theorem:
⇒ x + z = 180°
⇒ x + 110° = 180°
⇒ x = 180° - 110°
⇒ x = 70°
