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I've tried doing it but I end up only constructing 135 degree angle.I have to use ruler without divisions and compass.It must be done with system of isosceles and equilateral triangle and their properties ,e.g external angle and etc. and the bisector.

Can you give me directions? Thank You in advance!

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    $A$ general remark that applies to several of the comments and answers: A lot of effort was expended trying to tell a 7th-grader what is and isn't possible with ruler and compass, which is something that us mathematicians are interested in for historical and theoretical reasons, and comparatively little effort was expended to first establish whether that had anything to do with what she or he was actually trying to do.2011-04-20

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At the level of elementary geometry, I'd guess that it was a typo and that you are expected to compute a 135 degree angle. It's not immediately obvious, but can be figured out pretty easily (as you have already done) once you figure out what 135 degrees really looks like.

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    did you read the first sentence to the question? `:p`2011-04-20
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If you can construct a 145 degree angle then you can construct a 55 degree angle by removing 90 degrees, and so a 10 degree angle, by removing 45 degrees. It is a classical theorem that a 10 degree angle cannot be constructed with ruler and compass. See http://en.wikipedia.org/wiki/Angle_trisection#Angles_may_not_in_general_be_trisected

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    So yes, allowing trisections... you could do a neusis construction or use a carpenter's square, or a number of other devices...2019-01-08
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You cannot do it with an umarked ruler and compass.

Here is a way with a markable ruler and compass.

  1. construct a 30 degree angle (bisect an equilateral triangle) and call the vertex $O$
  2. draw a circle with centre $O$ and call where it meets the sides of the angle $A$ and $B$
  3. mark the ruler with the radius of the circle
  4. extend the line segment $AO$ beyond $O$, calling where it meets the circle again $C$, and then extend the line further beyond $C$
  5. place the ruler so that it touches $B$, and so that it cuts the circle again and the extended line the distance apart marked on the ruler, then draw the line and calling these points $D$ and $E$ respectively
  6. use what you know about angles and the isosceles triangles $BOD$ and $ODE$ to find the angle $OED$ (10 degrees)
  7. add a right angle (90 degrees) and half a right angle (45 degrees) at E to get a total angle of 145 degrees ($10+90+45$)
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    `You cannot do it with an umarked ruler and compass.` ,so maybe the math problem condition is incorrect.I think that they mean 135 degree angle ,which is very easy for me.Thank You!2011-04-20