# Question Video: Finding the Measure of an Angle given Its Arcβs Measure Using Another Inscribed Angle by Solving a Linear Equation Mathematics

Given that πβ πΉπΈπ· = 14Β° and πβ πΆπ΅π΄ = 2π₯ β 96Β°, calculate the value of π₯.

01:19

### Video Transcript

Given that the measure of angle πΉπΈπ· is equal to 14 degrees and the measure of angle πΆπ΅π΄ is equal to two π₯ minus 96 degrees, calculate the value of π₯.

So letβs look at the diagram. We quickly see that arc π΄πΆ is congruent to arc π·πΉ. And we know that inscribed angles subtended by congruent arcs are going to be equal in measure. So this means that angle π΄π΅πΆ is going to be equal in measure to angle π·πΈπΉ. Weβre in fact told that the measure of angle π΄π΅πΆ or πΆπ΅π΄ is two π₯ minus 96. And the measure of angle πΉπΈπ·, which is the same as π·πΈπΉ, 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 πΉπΈπ· and πΆπ΅π΄, we can deduce that π₯ is equal to 55.