Problem Solving

Hello good people.

A quick question for you experts... <Please refer to the picture>

In the picture, if o is the center of the circle and angle ABO = Angle OBC = 30, then is it true that angle X is 120? If you could you please give an explanation on how its true.. Just wanted get my fundamentals clear!!!

Thanks a lot

This is my first posting here - hope it makes sense.

Sides of the triangles are both radii of the circle and are therefore equal making these isocoles triangles.
Therefore angle A = 30 degrees and the angle AOB = 180-30-30 = 120 so the opposing angle must be 60 dgerees.
These 2 opposing angles are the angle X so X must be 120 degrees.

There is a geometry theorem which states that:

Angle subtended by the major arc at the center is twice the angle subtended by it at the circumference.

So, simply x = 2(30+30)

x= 2*60 = 120

Hope it is clear now