#### 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.