### Video Transcript

Are the two polygons similar?

Two polygons are similar if the corresponding angles are equal in measure and their corresponding side lengths are proportional. So we need to find the measure of angle ๐ด and the measure of angle ๐ธ. Each polygon should have all of the angles adding up to be 360 degrees. So to find the measure of angle ๐ด, we need to take 360 degrees and then subtract all of the three angles we already know, and then the remainder will be left for angle ๐ด. So weโre subtracting 103 degrees, 84 degrees, and 95 degrees. So the measure of angle ๐ด is 78 degrees.

Now, in the other polygon, the measure of angle ๐ธ, we would do the exact same thing. So after subtracting the three angles from 360, we get 95 degrees. So the measure of angle ๐ด is equal to the measure of angle ๐น, so theyโre both 78 degrees. Angle ๐ต and angle ๐บ are both 103 degrees, angle ๐ถ and angle ๐ป are both 84 degrees, and then lastly angle ๐ท and angle ๐ธ are both 95 degrees. This means our corresponding angles are equal in measure.

Now, letโs check if the side lengths are proportional. ๐ด๐ต to ๐น๐บ is 20 to 14, ๐ต๐ถ to ๐บ๐ป is just 16 to 11, ๐ถ๐ท to ๐ป๐ธ is 20 to 14, and ๐ท๐ด to ๐ธ๐น is 18.6 to 13. So we need to check if each of these fractions are proportional; do they reduce to be the exact same number? Unfortunately, they are not. These fractions do not reduce to be the exact same fraction; theyโre not proportional. Since the side lengths are not proportional, the polygons are not geometrically similar.