`A B C D` is a cyclic quadrilateral in which `/_B A D=75^0,\ /_A B D=58^0a n d\ /_A D C=77^0,\ A C\ a n d\ B D` intersect at `Pdot` then, find `/_D P C`

Explanation

`ABCD`, is a cyclic quadrilateral
`/_BAD+/_BCD=180^0`
`75^0+/_BCD=180^0`
`/_BCD=180^0-75^0=105^0`
`/_ADC+/_ABC=180^0`
`77^0+/_ABC=180^0`
`/_ABC=180^0-77^0=103^0`
`/_DBC=/_ABC-/_ABD`
`=>103^0-58^0=45^0`
`arc AB` subtends `/_ABD \and\ /_ACD` is the same segment.
`/_ABD=/_ACD=58^0`
`/_ACB=/_BCD-/_ACD=105^0-58^0=47^0`
Now in ,`/_\PBC` , ext. `/_DPC=/_PBC+/_PCB`
`=>/_DBC+/_ACB=45^0+47^0=92^0`
Hence, `/_DPC=92^0`