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1) We know that if [itex]\theta[/itex] is trisectible (with straightedge and compass), then [itex]\theta[/itex]/3 is constructible.

If so, then I can say that since 15

2) Let m,n be integers.

Then m|3n

and n|28n

I spent half an hour thinking about this, but I still have no clue...

Why are the implications (=>) true? Can someone please explain?

3) How can I prove that the acute angle whose cosine is 1/10 is constructible?

I know that if [itex]\theta[/itex] is constructible, then cos[itex]\theta[/itex] is constructible. But

Any help is appreciated!

**But is it also true that if [itex]\theta[/itex]/3 is constructible, then [itex]\theta[/itex] is trisectible (with straightedge and compass)?**If so, then I can say that since 15

^{o}is constructible, we have that 45^{o}is trisectible, right? (because we can copy an angle of 15^{o}three times, thus trisecting the angle 45^{o})2) Let m,n be integers.

Then m|3n

^{3}=> m|nand n|28n

^{3}=> n|mI spent half an hour thinking about this, but I still have no clue...

Why are the implications (=>) true? Can someone please explain?

3) How can I prove that the acute angle whose cosine is 1/10 is constructible?

I know that if [itex]\theta[/itex] is constructible, then cos[itex]\theta[/itex] is constructible. But

**is the converse true?**Why or why not?Any help is appreciated!

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