Question

find the lettered angle in each case

Answer 1

x=70 vertically opposite angle
y=110-70=40. Exterior angle property
z=180-110 angle sum
=70

Answer 2

angle BAC = angle FAE (vertically opp. angle)
angle BAC = x = 70°

angle BCA + angle ACD = 180° (linear pair)
z + 110 = 180°
angle BCA = z = 70°

angle BCA + angle ABC + angle BAC = 180° ( sum of angles of a triangle is equal to 180°)

z + y + x = 180°
70° +70° +y = 180°
angle ABC = y = 40 °

x = 70°
y = 40°
z = 70°

Hope it helps!!!