Question

Q8 In the given figure, O is the centre of the circle. If angle boc = 120°, then find the value of x .​

Answer 1

Answer: ∠AOC + ∠COB = 180° [because they are the linear pair]

Now, we need to find the value of ∠AOC by substituting the value of ∠COB. As the value of ∠COB is given as 120°. So,

∠AOB + ∠COB = 180°

∠AOB + 120° = 180°

∠AOB = 180° - 120°

∠AOB = 60° ..(I)

∴ The measure of angle AOB = 60°

Now, Since the angle subtended by an arc at the center of the circle is double the angle subtended by it on any remaining point of the circle, we have

∠AOC = 2 × ∠ADC

So, ∠ADC will be half of ∠AOC

⇒ ∠ADC = 1/2 ∠AOC

⇒ ∠ADC = 1/2 × 60° [ Using(I)]

⇒ ∠ADC = 30°

Therefore the value of x that is ∠ADC = 30°.

Step-by-step explanation: