In the given figure, O is the centre of circle and ∠DAB=500
. Calculate the values of x and y
Answers
Answer:
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Step-by-step explanation:
It is given that O is the centre of the circle and ∠DAB=50
o
We know that the radii of the circle are equal
OA=OB
From the figure we know that
∠OAB+∠OBA+∠AOB=180
o
By substituting the values
50
o
+50
o
+∠AOB=180
o
On further calculation
∠AOB=180
o
−50
o
−50
o
By subtraction
∠AOB=180
o
−100
o
So we get
∠AOB=80
o
From the figure we know that AOD is a straight line
It can be written as
x=180
o
−∠AOB
By substituting the values
x=180
o
−80
o
By subtraction
x=100
o
We know that the opposite angles of a cyclic quadrilateral are supplementary
So we get
∠DAB+∠BCD=180
o
By substituting the values
50
o
+∠BCD=180
o
On further calculation
∠BCD=180
o
−50
o
By subtraction
y=∠BCD=130
o
Therefore the value of x is 100
o
and y is 130
o
.