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Maharashtra State BoardSSC (English Medium) 9th Standard

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

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Question

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

Sum

Solution

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°

shaalaa.com
Remote Interior Angles of a Triangle Theorem
  Is there an error in this question or solution?
Chapter 3: Triangles - Practice Set 3.1 [Page 28]

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