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 110∘respectively.
∠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 110∘respectively.
