Question

If O is the centre of a circle.find the values of x and y where CD || AB. and ABC = 25°​

Answer 1

Answer:

We know that ∠BCD and ∠ABC are alternate interior angles

∠BCD=∠ABC=25

o

We know that the angle subtended by an arc of a circle at the center is double the angle subtended by the arc at any point on the circumference

∠BOD=2∠BCD

It is given that ∠BCD=25

o

So we get

∠BOD=2(25

o

)

By multiplication

∠BOD=50

o

In the same way

∠AOC=2∠ABC

So we get

∠AOC=50

o

From the figure, we know that AB is a straight line passing through the centre

Using the angle sum property

∠AOC+∠COD+∠BOD=180

o

By substituting the values

50

o

+∠COD+50

o

=180

o

On further calculation

∠COD+100

o

=180

o

By subtraction

∠COD=180

o

−100

o

so we get

∠COD=48

o

We know that

∠CED=

2

1

∠COD

So we get

∠CED=

2

80

o

By division

∠CED=40

o

Therefore, ∠CED=40

o