### Video Transcript

In the given figure, find the measure of the arc π΄πΆ plus the measure of the arc π΅π·.

Letβs look carefully at the diagram weβve been given. We have two chords, π΄π΅ and πΆπ·, which intersect inside a circle. Weβre given the measure of one of the angles formed at the point of intersection and asked to find the sum of the measures of the arcs π΄πΆ and π΅π·, which are the arcs now highlighted in orange and pink on our diagram.

To answer this question, we need to recall a theorem about the measures of angles formed by two chords that intersect inside a circle. This tells us that the measure of an angle between two chords is one-half the sum of the measures of its intercepted arc and its opposite arc. In this figure, the arc intercepted by the angle of 112 degrees is the arc π΅π·. And its opposite arc or the arc intercepted by its opposite angle is the arc π΄πΆ.

We can therefore form an equation. 112 degrees is equal to one-half the measure of the arc π΄πΆ plus the measure of the arc π΅π·. And thatβs great, because it is the measure of the arc π΄πΆ plus the measure of the arc π΅π· that weβre looking to find. We can work this out by multiplying both sides of the equation by two. This gives 224 degrees is equal to the measure of the arc π΄πΆ plus the measure of the arc π΅π·.

So by recalling the angles of intersecting chords theorem, we found that the measure of the arc π΄πΆ plus the measure of the arc π΅π· is 224 degrees.