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Question

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


Solution

∠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         
+ 80∘ + 40∘ = 180  
⇒ + 120∘ = 180 
⇒ x = 60  
Hence, the values of xy and z are 60, 80 and 40respectively.

Mathematics
Mathematics Part - II (Solutions)
Standard IX

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