# Question Video: Finding the Sum of Two Inscribed Arcs between Two Intersecting Chords given the Angle between the Chords Mathematics • 11th Grade

In the given figure, find the measure of arc π΄πΆ + the measure of arc π΅π·.

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### Video Transcript

In the given figure, find the measure of arc π΄πΆ plus the measure of arc π΅π·.

Letβs see what we know. By looking at the figure, we can see that line segment π΅π΄ and line segment πΆπ· are chords that intersect inside a circle, which means we can think about the angles of intersecting chords theorem. Which tells us that the measure of angle one is equal to one-half the measure of arc ππ plus the measure of arc ππ. In our figure, weβre interested in the measure of arc π΄πΆ plus the measure of arc π΅π·.

Based on what we know about intersecting chords in a circle, we can say that 112 degrees is equal to one-half times the measure of arc π΄πΆ plus the measure of arc π΅π·. And if we multiply both sides of this equation by two, we would have 224 degrees is equal to the measure of arc π΄πΆ plus the measure of arc π΅π·. And thatβs what weβre looking for, the measure of arc π΄πΆ plus the measure of arc π΅π·, which is 224 degrees.