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प्रश्न
In the given figure, line AB || line DE. Find the measures of ∠DRE and ∠ARE using given measures of some angles.
उत्तर
AB || DE and AD is a transversal line.
∠BAR = ∠RDE = 70° ...(Alternate angles)
And line AD is their transversal
∴ ∠BAD ≅ ∠EDA ...(Alternate angles)
∠BAD = 70° ...(Given)
∴ ∠EDA = 70°
In other words ∠EDR = 70° ...(A-R-D)
∠ARE, ΔRDE exterior angle
∴ ∠ARE = ∠EDR + ∠DER ...(remote interior angle theorem)
∴ ∠ARE = 70° + 40°
∴ ∠ARE = 110°
∠ARE + ∠DRE = 180° ...(angles in linear pair)
∴ 110° + ∠DRE = 180°
∴ ∠DRE = 180° - 110°
∴ ∠DRE = 70°
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