Question

In the given figure, measures of some angles are given. Using the measures find the values of x, y, z.

Answer 1

∠NEM + ∠NET = 180^∘ (Linear angle property)
⇒ y + 100^∘ = 180^∘
⇒ y = 80^∘
Also, ∠NME + ∠EMR = 180^∘ (Linear angle property)
⇒ z + 140^∘ = 180^∘
⇒ z = 40^∘
Now, In △NEM
∠N + ∠E + ∠M = 180^∘ (Angle sum property)
⇒ x + y + z = 180^∘
⇒ x + 80^∘ + 40^∘ = 180^∘
⇒ x + 120^∘ = 180^∘
⇒ x = 60^∘
Hence, the values of x, y and z are 60^∘, 80^∘ and 40^∘respectively.