Read the given question and decide which of the following information is sufficient to answer the question.

Question:

What is the value of  $$\theta$$​?

Information:

(1)  O is the center of the circle

(2) 0 < $$\theta$$​ < 90$$^o$$​​

Correct option is C

Information:

1) The circle has center O. ∠COA = 30° and ∠AOB = θ (as shown in the diagram).
2) It is also given that 0° < θ < 90°.

Concept Used:

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle..

Solution:

Using the angle at center and angle at circumference property of circles:
Given ∠COA = 30°, and O is the center,
=> $$θ = 2 × ∠COA = 2 × 30° = 60°$$​​
Hence, the value of θ is 60°.

Final Answer: Only Statement (1) alone is sufficient to answer the question.