Draw a circle. Mark an arc LMN on this circle. Inscribe an angle LMN in it.

How many more angles can you inscribe in this arc?

In an arc LMN

The vertex M is on the arc

And the endpoints L AND M are on arms of ∠ LMN

Hence ∠ LMNis inscribed on arc LMN

∴ There can be infinite points on arc LMN

And ∴ Infinite number of angles can inscribed in arc LMN

which are passing through end points L & M