Question Video: Finding the Measure of an Arc Given Its Equal Arcβs Measure Mathematics

Find π arc π΅πΈ, where π is the center of the circle.

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Video Transcript

Find the measure of arc π΅πΈ, where π is the center of the circle.

First, letβs identify arc π΅πΈ. After we highlight arc π΅πΈ, itβs important to notice that the segment π΅π΄ and the segment πΈπΆ are two parallel chords in this circle. We know by the measures of arcs between parallel chords theorem that the measure of the arcs between parallel chords of a circle are equal. This means that the arc π΅πΈ will be equal in measure to the arc π΄πΆ. We can also see that line segment π·πΆ intersects line segment π΅π΄ at the center of the circle π.

We can therefore say that angle π΄ππΆ is the opposite or vertical angle from angle π΅ππ· and is, therefore, also equal to 39 degrees. Since π is the center of the circle and arc π΄πΆ is subtended by the angle π΄ππΆ, we can say that the arc measure is equal to the central angle measure, which is 39 degrees. Since arc π΄πΆ is 39 degrees, arc π΅πΈ must also be equal to 39 degrees.