Question

in given figure o is the centre of the circle find the value of x

Answer 1

in figure,
angle CAD=x
angle BCD=2x

we know according to circle concept ,
angle CAD = angle CBD
so,
angle CBD=x

also line BC contains center of circle hence triangle CDB is right angle triangle.
hence,
angle CDB= 90 degree

now
we know ,
sum of all angles of triangle is equal to 180 degree .
so,
angle BCD +angle CBD +angle CDB=180
2x + x +90 =180

=> 3x=180-90

=> x=90/3

=> x=30 degree

Answer 2

Given
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a circle with centre 'O'
∠CAD=x and
∠BCD=2x
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To prove / find
The value of 'x'
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Proof
we know that ∠CAD=∠BCD = x because of property of a circle
and as BC is the diameter CDB is right angle triangle. it forms 90 degree

∠CDB = 90

in triangle BCD

∠CBD + ∠BCD + ∠CDB = 180

90 + 2X + X = 180

3x = 90

x = 30
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∠CAD=30

∠BCD = 60