WEBVTT
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Is the quadrilateral ๐ด๐ต๐ถ๐ท cyclic?
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We can begin by reminding ourselves that a cyclic quadrilateral is a quadrilateral with all four vertices inscribed on a circle.
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One property of cyclic quadrilaterals is that opposite angles are supplementary.
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We can check if a quadrilateral is cyclic by checking if opposite angles are supplementary.
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So letโs have a closer look at the figure that weโre given.
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The angle which is opposite to this given angle of ๐ด๐ต๐ถ would be the angle at ๐ท.
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If the angle at ๐ท and this angle at ๐ต add to 180 degrees, then ๐ด๐ต๐ถ๐ท would be cyclic.
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So letโs see if we can indeed work out the measure of this angle.
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We are given that the measure of angle ๐น๐ถ๐ท is 49 degrees.
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And we can observe that the angle measure at ๐ธ๐ถ๐น is marked as congruent.
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Itโs also 49 degrees.
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The total angle measure then of angle ๐ธ๐ถ๐ท will be 49 degrees plus 49 degrees, which is 98 degrees.
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We can then use the fact that we have a pair of parallel lines.
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And so angle ๐ด๐ท๐ถ is alternate to angle ๐ธ๐ถ๐ท.
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Itโs also 98 degrees
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Letโs remember that weโre checking if opposite angles are supplementary.
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Well, when we add together 98 degrees and 82 degrees, we do indeed get 180 degrees.
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So that means that opposite angles are supplementary.
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And so we can give the answer yes, since ๐ด๐ต๐ถ๐ท is cyclic.