In circle a below, ∠bae ≅ ∠dac. circle with center a and points b, c, d, e are labeled counterclockwise. angle bae and angle dac are marked congruent. arc be is labeled 12 x minus 10 degrees and arc dc is labeled 5 x plus 53 degrees. what is the marc bcd? a. 82° b. 98° c. 164° d. 180°

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.

Option a : week- amuont paid