Question Video: Finding the Measure of an Inscribed Angle between Two Intersecting Chords given the Inscribed Arcs Mathematics

Find š‘„.

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Video Transcript

Find š‘„.

In this question, weā€™re asked to find the value of š‘„. And we can see that š‘„ is the angle between two chords in our circle. Thatā€™s the chord š“šµ and the chord š¶š·. We can recall the following fact. The angle between two chords in a circle is one-half the sum of the measures of the arcs opposite the angle. And in our diagram, weā€™re given the measures of both of the arcs opposite our angle š‘„. Thatā€™s the arc š“š¶, which has measure 73 degrees, and the arc š·šµ, which has measure 133 degrees. So by applying this result, we must have that š‘„ is equal to one-half times 73 degrees plus 133 degrees. We can then evaluate this expression. 73 plus 133 is 206, and then one-half of this is 103 degrees.

Therefore, we were able to show that if š‘„ is the angle shown in the diagram, š‘„ is equal to 103 degrees.

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