1.

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

Answer»

i. ∠B AD = 70°, ∠DER = 40° [Given] 

line AB || line DE and seg AD is their transversal. 

∴ ∠EDA = ∠BAD [Alternate Angles] 

∴ ∠EDA = 70° ….(i) 

In ∆DRE, 

∠EDR + ∠DER + ∠DRE = 180° [Sum of the measures of the angles of a triangle is 180°] 

∴ 70°+ 40° +∠DRE = 180° [From (i) and D – R – A] 

∴ ∠DRE = 180° - 70° - 40° 

∴ ∠DRE = 70°

ii. ∠DRE + ∠ARE = 180° [Angles in a linear pair] 

∴ 70° + ∠ARE = 180° 

∴ ∠ARE = 180°- 70° 

∴ ∠ARE =110° 

∴ ∠DRE = 70°, ∠ARE = 110°



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