Question

Find x,y,z
Please answer this

Answer 1

∠O= 65° (VERTICALLY OPPOSITE ANGLES)
now, consider ΔAOB
∠AOB+∠ABO+∠BAO= 180° ( angle sum property)
65°+ ∠y+35°= 180°
100°+∠y=180°
∠y= 180°- 100°
∠y=80°
AB║CD
∴∠DAC=BCA (ALT. INT. ANGLES)
∴∠z=40°
∠AOB+∠BOC= 180° (LINEAR PAIR)
∴65°+∠BOC=180°
∠BOC= 180°- 65°
∠BOC=115°

IN ΔBOC:
∠BOC+∠BCO+∠CBO= 180° (ANGLE SUM PROPERTY)
115°+40°+∠x= 180°
∠x+150°=180°
∠x=180°-155°
∴∠x=25°


∴∠x=25°; y=80°; z=40°

Answer 2

$x = 25.y = 80.z = 40$