Question

If O is the centre of circle show in fig given and angleAOB = 110°, Then Find angleBCD.​

Answer 1

angle AOB=100

angle ACB=50(angle made at center is double the angle made at any point)

Now,ACBD is cyclic quadrilateral

So, angle ADB+angle ACB=180

therefore,angle ADB=180-50=130

answer is 130

Answer 2

The value of ∠BCD= 55°

Step-by-step explanation:

Given : ∠AOB=110°

To find: ∠BCD

As we know

reflex(∠AOB) = 360°-∠AOB

                      = 360°-110°   = 250°

Now as we know : The angle subtended by arc at the centre is double than angle subtended by it at any point on the remaining part of the circle.

Therefore $\angle ACB= \dfrac{1}{2} \text{ Reflex of}\angle AOB= \dfrac{1}{2} \times 250^\circ= 125^\circ$

Now as we can see

∴ ∠ACB+∠BCD= 180°

⇒ 125°+∠BCD= 180°

⇒∠BCD= 180°-125°= 55°

Hence the ∠BCD= 55°

#Learn more

In the figure , O is the centre of the circle. Find ∠CBD

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