Question

In a cyclic quadrilateral ABCD, if AB =AD, angle DAC = 60° and angle BDC = 50°
then what is the value of angle ACD?In a cyclic quadrilateral ABCD, if AB =AD, angle DAC = 60° and angle BDC = 50°
then what is the value of angle ACD?

Answer 1

Answer:

ACD=60°

Step-by-step explanation:

because in the quadrilateral are all sides are unequal hence in triangle AB=DB hence. If BDC is equalizes to a triangle

Answer 2

Given : In a cyclic quadrilateral ABCD, if AB =AD, angle DAC = 60° and angle BDC = 50°

To find : what is the value of angle ACD

Solution:

AB = AD

=> ∠ADB = ∠ABD

∠BAC =  ∠BDC    ( angle by same chord BC)

=> ∠BAC = 50°

∠DAC = 60°

∠DAB = ∠DAC + ∠BAC = 60° + 50° = 110°

in Δ ABD

∠DAB + ∠ADB + ∠ABD  = 180°

=> 110°+  ∠ABD + ∠ABD  = 180°

=> 2∠ABD  =70°  

=> ∠ABD  =35°  

∠ACD =  ∠ABD   ( angle by same chord AD)

=> ∠ACD =   35°  

value of angle ACD =  35°    

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