### Video Transcript

In the figure, line segment π΄πΈ
and line segment π΅πΆ pass through the midpoint of the circles. Given that the measure of angle
πΉπΈπ· is 50 degrees and the measure of angle πΆπ΅π΄ is equal to two π₯ minus 10
degrees, find π₯.

We begin by adding the relevant
measurements to our diagram. πΉπΈπ· is 50 degrees, and πΆπ΅π΄ is
two π₯ minus 10 degrees. Now, we do know that angles
subtended from the same arc are equal. But we also know that angles
subtended from arcs with equal measure are equal. And this is really useful when
weβre working with a pair of concentric circles, because weβre able to say that the
measure of arc πΉπ· is equal to the measure of arc πΆπ΄. Theyβre both equal to this angle
here. Since the measure of those two arcs
are equal, then the measure of any angles subtended from the arcs must also be
equal. In other words, the measure of
angle πΉπΈπ· must be equal to the measure of angle πΆπ΅π΄.

And so, we can say that 50 must be
equal to two π₯ minus 10. Then, we simply have an equation
that we can solve for π₯. Weβll begin by adding 10 to both
sides, giving us 60 equals two π₯. And then we divide through by two,
giving us 30 is equal to π₯, or π₯ is equal to 30.