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Geometry Level 2

In figure, Angle ACB is right angle & AC=CD & CDEF is Parallelogram .If Angle FEC=10,then Calculate angle BDE...


The answer is 50.

Archiet Dev by Archiet Dev , 20, India

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3 solutions

Aya Alaa
Jul 20, 2014

as CDEF is Parallelogram and CEF=10 , DEC=90 so DEF=100 , EDC=80 AS DC=AC then CDA=DAC=50 when DCA=80 AS DE IS Parallel TO AC THEN BDE=180-(EDC+CDA) =180-(80+50)=50

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Awnon Bhowmik
Jul 11, 2014

Angle ECD = 10 (Alternate Angle)

Angle ACD = 90 - 10 = 80 (Complementary Angle)

AC = CD So the base angles are equal, let them be x Then 2x + 80 = 180, or x = 50

Angle CDE = 90 - 10 = 80

Angle BDE = 180 - 50 - 80 = 50 (Sum of angles on a straight line)

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Archiet Dev
Jun 2, 2014

Angle FEC = Angle ECD

Thus An.(Angle) ACD = (ACB - ECD) 

                       =>    ACD = 90-10  

                        =>   80

In Triangle ACD we have, 

                        An.CAD = An.ADC = x (Isosceles Triangle Property)

Thus,An.ACD= 80

So, x + x + 80 = 180 =>x = 50

Now in Triangle CEF =>An .ECF =90

=>An.FEC =10

So,An.CFE = 80 = An.CDE (Opposite angles of llgm are equal)

=>An.(ADC + CDE + BDE) = 180(Linear pair)

=>50 + 80 + BDE =180

=>An. BDE = 50

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