Hi Nikunj,

I am posting the question below with the image. I am sorry about the inconvenience.

In the figure shown, point O is the center of semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60
(2) The degree measure of angle BCO is 40

Explanation:

Try to jot down the given information,

Given, BO=CO=radius=AB –> triangles BOC and ABO are isosceles.

∠BAO=∠BOA and ∠BCO=∠CBO

∠CBO=2∗∠BAO. This is because of exterior angle theorem. In a triangle, exterior angle is equal to sum of the other two internal angles.

Statement I is sufficient: The degree measure of angle COD is 60º.

∠BAO+∠ACO=∠COD=60º degrees (Using exterior angle theorem)

∠ACO=∠CBO=2∗∠BAO

So,∠BAO+∠ACO=2∗∠BAO+∠BOA=3∗∠BAO=60º

∠BAO=20º.

Sufficient.

Statement II is sufficient: The degree measure of angle BCD is 40º:

∠BCO=40º –> ∠BCO=∠CBO=40º=2∗∠BAO –> ∠BAO=20º.

Sufficient.

So the Answer is D.

Hope this helps.