Question

Find x + y + z + w from the below figure :

Answer 1

∠r + 120° + 80° + 60° = 360° [Angle sum property of a quadrilateral]
∠r + 260° = 360°
∠r = 360° – 260° = 100°
Now x + 120° = 180° (Linear pair)
x = 180° – 120° = 60°
y + 80° = 180° (Linear pair)
⇒ y = 180° – 80° = 100°
z + 60° = 180° (Linear pair)
⇒ z = 180° – 60° = 120°
w = 180° – ∠r = 180° – 100° = 80° (Linear pair)
x + y + z + w = 60° + 100° + 120° + 80° = 360°