Video: Determining Whether a Given Quadrilateral Is Cyclic

Is 𝐴𝐡𝐢𝐷 a cyclic quadrilateral?

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Video Transcript

Is 𝐴𝐡𝐢𝐷 a cyclic quadrilateral?

In any cyclic quadrilateral, we know that the opposite angles sum to 180 degrees. As angles 𝐴 and 𝐢 are opposite, this would mean that angle 𝐴 plus angle 𝐢 must be equal to 180 degrees. 79 degrees plus 62 degrees is equal to 141 degrees. This means that angle 𝐴 plus angle 𝐢 is not equal to 180 degrees. We can therefore conclude that the answer is no, 𝐴𝐡𝐢𝐷 is not a cyclic quadrilateral, as the sum of angles 𝐴 and 𝐢 is not 180 degrees.

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