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°.

c.) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.

Step-by-step explanation:

Line segment DB divides <ADC into two congruent angles. That is:

<ADB is congruent to <CDB

Segment DB of ∆ABD is congruent to segment DB of ∆CBD.

Also, Segment AD of ∆ABD is congruent to segment CD of ∆CBD.

This means two sides (DB and AD) and an included angle (<ADB) of ∆ABD are congruent to the corresponding two sides (DB and CD) and included angle (<CDB) of ∆CBD.

Therefore, by the SAS Congruence Postulate, ∆ABD is congruent to ∆CBD.