ABCD is a square and BCE is an equilateral triangle. Find the value of a, b and reflex angle BED.
Dear Student,
Please find below the solution to the asked query:
Given : ABCD is a square , So
ABC = BCD = CDA = DAB = 90 --- ( 1 )
And
BCE is a equilateral triangle , So
EBC = ECB = BEC = 60 --- ( 2 )
So,
DCE = BCD - ECB = 90 - 60 = 30 ( Substitute value from equation 1 and 2 )
As given BCE is a equilateral triangle , SO BC = EC = EB and ( AB = BC = CD = DA , Sides of square ) , So
EC = CD , Then triangle DEC is a isosceles triangle so from base angle theorem we get
CDE = CED --- ( 3 )
From angle sum property of triangle we get in triangle DEC :
CDE + CED + DCE = 180 , Substitute value from equation 3 we get
CED + CED + DCE = 180 , Now substitute values we get
b + b + 30 = 180
2 b = 150
b = 75 , So
CDE = CED = b = 75
Then ,
a = CDA - CDE = 90 - 75 = 15 ( Substitute value from equation 1 and CDE = 75 )
And
Reflex BED = 360 - BEC - CED = 360 - 60 - 75 = 225 .
therefore,
a = 15 , b = 75 and Reflex BED = 225 ( Ans )
Hope this information will clear your doubts about The Triangle and its Properties.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : ABCD is a square , So
ABC = BCD = CDA = DAB = 90 --- ( 1 )
And
BCE is a equilateral triangle , So
EBC = ECB = BEC = 60 --- ( 2 )
So,
DCE = BCD - ECB = 90 - 60 = 30 ( Substitute value from equation 1 and 2 )
As given BCE is a equilateral triangle , SO BC = EC = EB and ( AB = BC = CD = DA , Sides of square ) , So
EC = CD , Then triangle DEC is a isosceles triangle so from base angle theorem we get
CDE = CED --- ( 3 )
From angle sum property of triangle we get in triangle DEC :
CDE + CED + DCE = 180 , Substitute value from equation 3 we get
CED + CED + DCE = 180 , Now substitute values we get
b + b + 30 = 180
2 b = 150
b = 75 , So
CDE = CED = b = 75
Then ,
a = CDA - CDE = 90 - 75 = 15 ( Substitute value from equation 1 and CDE = 75 )
And
Reflex BED = 360 - BEC - CED = 360 - 60 - 75 = 225 .
therefore,
a = 15 , b = 75 and Reflex BED = 225 ( Ans )
Hope this information will clear your doubts about The Triangle and its Properties.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards