Question 6: In the given figure, line AB || line DE. Find the measures of ∠ DRE and ∠ ARE using given measures of some angles.

Question 6:

In the given figure, line AB || line DE. Find the measures of DRE and ARE using given measures of some angles.

Answer: 
AB || DE and AD is a transversal line.
∠BAR = ∠RDE = 70      (Alternate angles)
In △DER
∠D + ∠E + ∠DRE = 180   (Angle sum property)
⇒ 70 + 40 + ∠DRE = 180         
⇒ 110 + ∠DRE = 180 
⇒ ∠DRE = 70
Now, ∠ARE = ∠DRE + ∠RDE   (Exterior angle property)
= 70 + 40          
= 110
Hence, the measures of ∠DRE and ∠ARE are 70∘ and 110respectively.

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