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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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