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