Answer:
y = 40°
z = 140°
x = 100°
Information:
(i) Sum of interior angles of a triangle sum ups to 180°
(ii) On a straight line, the angles sum up to 180°
(iii) One exterior angle is equal to two opposite interior angles.
Solve for z
Here the exterior angle theorem applies.
∠z = 120° + 20°
∠z = 140°
Solve for y
Find the angle C. Here angles lie on a straight line.
∠? + 120° = 180°
∠? = 180° - 120° = 60°
80°, 60° and y are interior angles of a triangle.
y + 80°+ 60° = 180°
y = 180° - 140°
y = 40°
Solve for x
∠? = 40° (vertically opposite angle)
Now,
y + x + 40° = 180°
40° + x + 40° = 180°
x = 100°