# Question Video: Finding the Measure of the Inscribed Angle between Two Secants given the Measure of the Two Inscribed Arcs

Find the value of π₯.

01:14

### Video Transcript

Find the value of π₯.

In the given figure, line segment πΆπΈ and line segment π΄πΈ intersect at point πΈ. The angle created at their intersection is the one labeled π₯. 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 π·π΅ that measures 71 degrees and arc πΆπ΄ that measures 144 degrees.

Since the line segment πΆπΈ and the line segment π΄πΈ 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 πΆπΈπ΄, will be equal to one-half the difference of the two intercepted arcs. And that means we can say that π₯ is equal to 144 minus 71 divided by two. π₯ is equal to 36.5 degrees.