Video: Finding the Sum of Two Inscribed Arcs between Two Intersecting Chords given the Angle between the Chords

In the given figure, find the measure of arc 𝐴𝐢 + the measure of arc 𝐡𝐷.

01:14

Video Transcript

In the given figure, find the measure of arc 𝐴𝐢 plus the measure of arc 𝐡𝐷.

Let’s see what we know. By looking at the figure, we can see that line segment 𝐡𝐴 and line segment 𝐢𝐷 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 𝑃𝑆 plus the measure of arc 𝑄𝑅. In our figure, we’re interested in the measure of arc 𝐴𝐢 plus the measure of arc 𝐡𝐷.

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 𝐴𝐢 plus the measure of arc 𝐡𝐷. And if we multiply both sides of this equation by two, we would have 224 degrees is equal to the measure of arc 𝐴𝐢 plus the measure of arc 𝐡𝐷. And that’s what we’re looking for, the measure of arc 𝐴𝐢 plus the measure of arc 𝐡𝐷, which is 224 degrees.

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