Question

In the circle below, AB is segment tangent to circle C.
If angle DBC is 56 degrees, find the measure of angle BCD.

Answer 90 degrees
34 degrees
56 degrees
146 degrees

Answer 1

BCD = 180 - 56 - 90

Answer 2

since AB is the tangent to circle Cis perpendicular to CD
that is angleCDB =90degree (tangent perpendicular to radius)
therefore
angle BCD =180-angleCDB -56degree(angle sum of triangle)
= 180-90-56
=34degree