Question Video: Finding the Measure of an Inscribed Angle between Two Intersecting Chords given the Inscribed Arcs Mathematics

Video Transcript

Find 𝑥.

In this question, we’re asked to find the value of 𝑥. And we can see that 𝑥 is the angle between two chords in our circle. That’s the chord 𝐴𝐵 and the chord 𝐶𝐷. We can recall the following fact. The angle between two chords in a circle is one-half the sum of the measures of the arcs opposite the angle. And in our diagram, we’re given the measures of both of the arcs opposite our angle 𝑥. That’s the arc 𝐴𝐶, which has measure 73 degrees, and the arc 𝐷𝐵, which has measure 133 degrees. So by applying this result, we must have that 𝑥 is equal to one-half times 73 degrees plus 133 degrees. We can then evaluate this expression. 73 plus 133 is 206, and then one-half of this is 103 degrees.

Therefore, we were able to show that if 𝑥 is the angle shown in the diagram, 𝑥 is equal to 103 degrees.