#### 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)

⇒

⇒

Also, ∠NME + ∠EMR = 180∘ (Linear angle property)

⇒

⇒

Now, In △NEM

∠N + ∠E + ∠M = 180∘ (Angle sum property)

⇒

⇒

⇒

⇒

Hence, the values of

⇒

*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.
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