Question

A tangent-tangent angle intercepts two arcs that measure 149° and 211

What is the measure of the tangent-tangent angle?

Answer 1

31

Explanation:

did the test

Answer 2

31°

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

`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)`