Is my work correct? given: abcd is an inscribed polygon. prove: ∠a and ∠c are supplementary angles.

Check the picture below.

so, notice, the intercepted arc by the inscribed angle A is the red arc there, namely arcBCD, and the one intercepted by angle C is the arcBAD in blue there.

now, both arcs take up the whole circle, namely the whole 360°, and we also know that arcBCD = 2A, whilst arcBAD = 2C.

W-14=t. that i think is the answer idk