# Question Video: Using the Relationship Between Parallel Chords to Determine the Measure of an Arc Expressed Algebraically Mathematics

In the following figure, π΄π΅ and πΈπΉ are two equal chords, π΅πΆ and πΉπΈ are two parallel chords. If the measure of arc π΄πΆ = 120Β°, find the measure of arc πΆπΈ.

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### Video Transcript

In the following figure, π΄π΅ and πΈπΉ are two equal chords. π΅πΆ and πΉπΈ are two parallel chords. If the measure of arc π΄πΆ is 120 degrees, find the measure of arc πΆπΈ.

Letβs begin by using the fact that these two line segments π΄π΅ and πΈπΉ are two equal chords. Since theyβre equal in length, we can deduce that the measure of their arcs must also be equal. So the measure of arc π΄π΅ must be equal to the measure of arc πΈπΉ. In fact, weβre told that this is equal to π₯ degrees. Then, we use the information about π΅πΆ and πΉπΈ; theyβre parallel chords. This means that the measures of the arcs between those two chords is equal. That is, the measure of arc πΆπΈ must be equal to the measure of arc π΅πΉ. And this time weβre also told that that is equal to π₯ plus 30 degrees.

Using this information alongside the measure of arc π΄πΆ, we know that the sum of all the arc measures is 360 degrees. So we can form and solve an equation. The sum of the arcs is π₯ plus π₯ plus 30 plus π₯ plus π₯ plus 30 plus 120. And that must be equal to 360. And so that left-hand side simplifies to four π₯ plus 180. So four π₯ plus 180 degrees equals 360. We can therefore say that four π₯ must be equal to 180. And we can then solve for π₯ by dividing through by four. So π₯ degrees equals 45 degrees. We want to find the measure of arc πΆπΈ, and we said that that was equal to π₯ plus 30. So the measure of arc πΆπΈ is 45 plus 30, which is equal to 75 degrees. The measure of arc πΆπΈ then is 75 degrees.