Answer:
31°
Step-by-step explanation:
A tangent-tangent angle is the angle formed by two tangents to a circle (angle BCD in attached diagram).
Lines CB and CD are tangent to the circle, then angles ABC and ADC are right angles (with 90° measure).
Angle BCD intercepts two arcs that measure 149° and 211°, this means minor arc BD has the measure of 149° and major arc BD has the measure of 211°. If minor arc BD has the measure of 149°, then angle BAD has the measure 149° too.
The sum of all measures of interior angles of quadrilateral is always 360°, then
[tex]m\angle BCD+m\angle CBA+m\angle BAD+m\angle ADC=360^{\circ}\\ \\m\angle BCD=360^{\circ}-90^{\circ}-149^{\circ}-90^{\circ}\\ \\m\angle BCD=31^{\circ}[/tex]
