Q6 of 45 Page 27

In figure 3.10, line AB || line DE. Find the measures of ∠DRE and ∠ARE using given measures of some angles.

Given ∠DAB = 70° and ∠DER = 40°


In the given figure ∠DAB = ∠ADE [Alternate Interior angles are equal]


∴ ∠ADE = ∠RDE = 70°


In ΔDER,


∠DER + ∠DRE + ∠RDE = 180°


⇒ 40° + ∠DRE + 70° = 180°


⇒ ∠DRE = 180° - 110°


⇒ ∠DRE = 70°


∵ ∠ARE is an exterior angle of triangle DER


∠ARE = ∠RDE + ∠DER = 70° + 40°


⇒ ∠ARE = 110°


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