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ABCD is a cyclic quadrilateral where BC is diameter and angle ADC = 130 degree . Find the value of angle ACB?

1 Answer
Feb 1, 2017

Answer:

#angleACB=40^@#

Explanation:

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Given : #ABCD# lie on a circle, #angleADC=130^@, and BC# is the diameter.
We know that opposite angles in a cyclic quadrilateral add up to #180^@#,
#=> angleADC+angleABC=180^@#
#=> angleABC=180-angleADC=180-130=50^@#
As #BC# is the diameter,
#=> angleBAC=90^@#,
#=> angleACB=180-(angleABC+angleBAC)=180-(50+90)=40^@#

Alternatively, you can do it this way:
As #BC=# diameter, #BDC=90^@#,
#=> angleBDA=130-90=40^@#
#=>angleACB=angleBDA=40^@#