Amutant cucumber plant has flowers that fail to open when mature. crosses can be done with this plant by manually opening and pollinating the flowers with pollen from another plant. when closed x open crosses were done, all the f1 progeny were open. the f2 plants were 145 open and 59 closed. a cross of closed x f1 gave 81 open and 77 closed. how is the closed trait inherited? what evidence led you to your conclusion?

This trait is inherited according to  Mendel's principles and it posses a complete dominance, where open is dominant and closed is recessive.

Explanation:

First, there are closed-flowers plants and open-flowers plants. A cross between them produces only open flowers at F1. With this information, we can say that open condition is dominant over closed, and probably, parental plants were homozygous, like this:  

- Open flowers: FF

- Closed flowers: ff

- F1 open flowers: Ff

When F1 was crossed, the progeny was:

- 145 open

- 59 closed

When we cross two heterozygous, we obtain a phenotypical radio of 3:1, like this:

- (1) FF Open

- (2) Ff Open

-  (1) ff Closed

This ratio is very similar to the F2 above reported (145 open and 59 closed).

When F1 (Ff) plants were crossed with closed plants the progeny was:

- 81 open

- 77 closed

This is alike to a ratio 1:1.

In the Punnett Square, it is possible to notice that in this cross it is expected a ratio of 1:1 closed/open.

In conclusion, this trait is inherited according to  Mendel's principles and it posses a complete dominance, where open is dominant and closed is recessive.