Math, asked by anurag5248, 1 year ago

in figure 3.10 line ab parallel line de find the measures of angle Dr B and Angle A R using given measures of some angles

Answers

Answered by shubham85288
9
Since AB || DE,

∠EDA and ∠BAD are alternate interior angles.

⇒ ∠EDA  =  ∠BAD  =  70°
and , ∠EDR = ∠EDA = 70°

now, in the ΔRED ,

∠DRE + ∠RED  + ∠RDE = 180°   [ angle sum property of a triangle ]

∴  ∠DRE + 40° + 70°       = 180°

⇒ ∠DRE + 130°              = 180°

⇒ ∠DRE                          = 180° - 130° 

⇒ ∠DRE                          = 50°

now, 

∠DRE + ∠ARE = 180°         [ since AD is a straight line ]

⇒ 50° +  ∠ARE = 180°

⇒  ∠ARE          = 180° - 50° 

⇒ ∠ARE          = 130°

alternate method:
 
∠ARE is an exterior angle for ΔRED 

so ∠RED  + ∠RDE = ∠ARE  

⇒ 70° + 40°            = 130° = ∠ARE  

Answered by darshanjeyakuma
2

Hope this ans helps you



Since AB || DE,


∠EDA and ∠BAD are alternate interior angles.


⇒ ∠EDA  =  ∠BAD  =  70°

and , ∠EDR = ∠EDA = 70°


now, in the ΔRED ,


∠DRE + ∠RED  + ∠RDE = 180°   [ angle sum property of a triangle ]


∴  ∠DRE + 40° + 70°       = 180°


⇒ ∠DRE + 130°              = 180°


⇒ ∠DRE                          = 180° - 130° 


⇒ ∠DRE                          = 50°


now, 


∠DRE + ∠ARE = 180°         [ since AD is a straight line ]


⇒ 50° +  ∠ARE = 180°


⇒  ∠ARE          = 180° - 50° 


⇒ ∠ARE          = 130°


alternate method:

 

∠ARE is an exterior angle for ΔRED 


so ∠RED  + ∠RDE = ∠ARE  


⇒ 70° + 40°         


  = 130° = ∠ARE  



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