We have that the 2 arcs need to be equal, because their angles are the same. Hence, we get by setting the two expressions equal: 12x-10=5x+53 or 12x-5x=53+10 or 7x=63 or x=9. Hence, arce BE is equal to 12x-10=12*9-10=98 degrees. This is also equal to the arc DC. Since we have calculated arc DC, we only need to calculate arc BD (and sum those two). The total arcs of a circle are 360 degrees. Hence, EB+BC+DC+CE=360. But we have that BC+CE. So, we get: 98+BC+98+BC=360. Hence, we get that BC=CE(360-2*98)/2=82 degrees. Hence, BCD=98+82=180 degrees.
