Question

In the given figure , A triangle ABC is inscribed in a circle, and the tangent at C to the circle is parallel to the bisector of angle ABC. Find the magnitude of $\angle BCX$.(in degrees)

Answer 1

Let $\angle XCB=\theta °$

$\angle DAB$ is the angle in alternate segment of $\angle XCB$

So according to alternate segment theorem

$\angle XCB=\angle DAB=40°$

So $\angle BCX=40°$