Let AB and CD be two lines intersecting at a single point, say, P. APC and BPD, and APD and BOC form two pairs of vertically opposite angles. Additionally, ray AP is perpendicular on line CD. It implies the sum of APC and APD is equal to 180o. Now, the sum of angles APD and BPD is equal to 180o. By using these two equations, it’s clear that the sum of angles APC and APD is equal to the sum of APD and BPD angles. It implies angle APC is equal to BPD. Similarly, it can be shown that angle APD is equal to angle BPC.