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

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.