Determine if the statement is true or false
The figures below are similar

True

Step-by-step explanation:

The polygons given have 5 sides, so the sum of their interior angles is (5-2) * 180 = 540. Next, there are 4 pairs of corresponding sides. Writing those sides as a, b, c, and d, for each pentagon, we can write

540 = a + b + c + d + missing angle

540 = a + b + c + d + missing angle

As is shown here, if a, b, c, and d are the same, 540 - (a+b+c+d) = missing angle is the same as well. Therefore, there are 5 corresponding angle pairs for the two polygons. Furthermore, because there are only 5 angles for each polygon, and because having all corresponding angles be equal makes polygons similar to each other, the polygons given are similar

15.5

step-by-step explanation:

5

∑

n = 1

substitute n = 1, 2, 3, 4, 5 and sum the terms

= + + + 2² + 2³

= 0.5 + 1 + 2 + 4 + 8

= 15.5