In the figure, arc $ABC$ of the circle subtends angle of $130 °$ at the centre O. If AB is produced to D, then $∠ CBD$ will be:

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

60 °

65 °

70 °

130 °

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that arc

ABC

of the circle subtends angle of

130 °

at the centre O.
Question Image

From figure,

Reflex ∠ A O C + ∠ A O C = 360 ° ⇒ Reflex ∠ A O C + 130 ° = 360 ° ⇒ Reflex ∠ A O C = 230 °

As we know that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circle.
So,

Reflex ∠ A O C = 2 × ∠ A B C

⇒ ∠ A B C = 12 × Reflex ∠ A O C ⇒ ∠ A B C = 12 × 230 ° = 115 °

Now, we know the sum of all angles lying on a straight line is

180 ° .

⇒ ∠ C B D + ∠ A B C = 180 ° ⇒ ∠ C B D + 115 ° = 180 ° ⇒ ∠ C B D = 65 °

The value of

∠ C B D = 65 °

.
Hence, the correct option is 2.

Watch 3-min video & get full concept clarity