Answer: 35 degrees
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Explanation:
Inscribed angle ABC = 55 subtends the minor arc AC which is 110 degrees (use the inscribed angle theorem).
The inscribed angle BDC subtends the minor arc CB, which we'll call x for now.
The two minor arcs (AC and CB) combine to form the arc ACB. Note how this is a semicircle since AB is a diameter. For any semicircle, the arc measure is 180 degrees.
So,
(arc AC) + (arc CB) = arc ACB
110 + x = 180
x = 180-110
x = 70
This cuts in half to 35 which is the inscribed angle BDC, again we're using the inscribed angle theorem here.
