Question 5:
In the given figure, measures of some angles are given. Using the measures find the values of x, y, z.
Answer:
∠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.
⇒ 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.
