Find the value of 𝑥.
In the given figure, line segment
𝐶𝐸 and line segment 𝐴𝐸 intersect at point 𝐸. The angle created at their
intersection is the one labeled 𝑥. And as these lines have intersected
the circle, they have created two intercepted arcs. If we sketch the center of the
circle, we can show arc 𝐷𝐵 that measures 71 degrees and arc 𝐶𝐴 that measures 144
Since the line segment 𝐶𝐸 and the
line segment 𝐴𝐸 can both be described as secants of the circle, we can use the
angles of intersecting secants theorem. Which tells us the angle created by
the intersection of two secants, in this case, the measure of angle 𝐶𝐸𝐴, will be
equal to one-half the difference of the two intercepted arcs. And that means we can say that 𝑥
is equal to 144 minus 71 divided by two. 𝑥 is equal to 36.5 degrees.