Question

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

Answer 1

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.