Bc is tangent to circle d at point c. the measure of ∠bdc is 35º.
what is the measure of ∠dbc?

35º

55º

90º

180º

The angle formed between the point of the tangent line to the line drawn from the center of the circle is 90°, thus, ∠BCD is equal to 90°. We also know that the summation os all angles in a triangle is 180°, therefore, we can have the equation below in solving for the angle of DBC.
180°=∠BCD + ∠BDC +∠DBC
180°=90° +35°+∠DBC
∠DBC=55°
The answer is 55°.