### Video Transcript

Given that the measure of angle
πΉπΈπ· is equal to 14 degrees and the measure of angle πΆπ΅π΄ is equal to two π₯
minus 96 degrees, calculate the value of π₯.

So letβs look at the diagram. We quickly see that arc π΄πΆ is
congruent to arc π·πΉ. And we know that inscribed angles
subtended by congruent arcs are going to be equal in measure. So this means that angle π΄π΅πΆ is
going to be equal in measure to angle π·πΈπΉ. Weβre in fact told that the measure
of angle π΄π΅πΆ or πΆπ΅π΄ is two π₯ minus 96. And the measure of angle πΉπΈπ·,
which is the same as π·πΈπΉ, is 14 degrees. Since these angles are equal, we
can form and solve an equation in π₯. That is, two π₯ minus 96 equals
14. To solve for π₯, we add 96 to both
sides, giving us two π₯ is equal to 110. And finally, we divide through by
two, and that gives us π₯ is equal to 55. And so given the information about
angles πΉπΈπ· and πΆπ΅π΄, we can deduce that π₯ is equal to 55.