geometry constructing angles.?

Question

how do i construct a 105 degree angle?

Answer 1

If you know how to construct standard angles (60 degrees, 120 degrees and 90 degrees) and how to bisect angles, you can do the following.
Draw a 90 degree angle. Bisect it to get a 45 degree angle. Draw a 60 degree angle as an addition to the 45 degree angle. 60 degrees + 45 degrees = 105 degrees.

Answer 2

Draw a line segment of a given length.
Then go to one endpoint of that line segment and draw an
arc of that same length.

Go to the other endpoint of the original line segment and draw
an arc of the same length until it intersects with the first arc.

Simply connect each endpoint to the arcs' intersection using
a straightedge and you will have an equilateral triangle.

Copy any of the three angles and that is a 60 degree angle.

Next, draw a perpendicular angle. Bisect it. And copy it
onto one side of the 60 degree angle. That will give you an
angle of 105 degrees because half of a 90 degree angle is
45 degrees. You just constructed an angle = 60 + 45 = 105

Answer 3

Constuct a 60 degree angle and then add a 45 degree angle.

Construction of an equilateral triangle will give you a 60 degree angle. Costructing a 90 degree angle and then bisecting it will give you the 45 degree angle.

Answer 4

I'll assume that this angle has to be constructed using only the standard tools of a classical geometrical construction --- a straight-edge ruler and a compass.

First construct a 60 deg. angle by using a compass to construct an equilateral triangle. (You do this by marking off some length in a chosen direction. Then, from the two endpoints of that length --- which will be vertices of the desired triangle --- construct arcs with the same compass setting. Their intersection will determine the remaining vertex of an equilateral triangle having sides equal to the initially chosen length.)

Now either:

A. Construct another similar equilateral triangle adjacent to that first triangle. (The two adjacent angles would add up to 120 deg.)

Bisect the second such 60 deg. angle, adjacent to the original 60 deg. angle. The 30 deg. angle now added to the original 60 deg angle gives you a 90 deg, angle, while leaving ONE MORE 30 deg. angle. By bisecting THAT last 30 deg. angle, you will now have an angle of

(60 + 30 + 15) degs. = 105 degs. QED

Or:

B. A less elegant way to proceed instead of doing what is described in method A is to "add a 45 deg. angle" to the original 60 deg. angle. You can do that by first erecting a perpendicular to one of the sides of the equilateral triangle, through a vertex.

(To do this, extend a side of the triangle through the vertex, in the opposite direction. You might as well make that extension long enough so that you can mark off another equal length on it. From the points so defined, now at equal distances from the vertex, you draw larger but equal size arcs that will intersect one another at a convenient point reasonably far away (but not too much!) from the chosen vertex. Join that point of intersection to the chosen vertex, and you'll have a 90 deg. angle with respect to a side of the triangle. Now bisect that 90 deg. angle! That gives you two 45 deg. angles. One of them, adjacent to one of the original 60 deg. angles, gives you there an angle of 60 deg. + 45 deg.= 105 deg.)

Method A is more elegant than method B because having constructed an equilateral triangle with only a few strokes in the first place, it repeats that and uses simple successive bisections of angles already present to obtain the 105 deg. angle.

Method B goes off with a completely different and to some extent more contrived construction, in order to produce a quite independently derived 45 deg. angle to "add" to the original 60 deg. angle. This break in the approach makes the full construction much more contrived.

Another reponder suggests that you "copy" a 45 deg. angle from somewhere else. In assessing the desirability of doing that, you may want to ponder the following. In classical geometrical constructions with a compass and ruler, "copying" angles is frowned upon, and even forbidden by purists, who would have you construct everything needed, from scratch, in the place where you need it.

Live long and prosper.

Answer 5

Use a protractor (which is a flat piece of plastic in the shape of a 1/2 circle) graduated from 0 to 180 degrees in 1 degree increments.
Find 105 on it and make a mark on your paper.
With the flat side of the protractor draw a line through the dot to the center point of the protractor.

If you have both standard drafting triangles (i.e. 30-60-90 and
45-90-45) put the 60 angle down and put a 45 degree angle on top of it and you'll have 105 degrees.

Answer 6

It goes 15 degrees past a perpedicular 90 degree line...

L <--- that is 90 degrees.

\_ <--- that is about 105 degrees.

Answer 7

hey man!,you could use a protratctor ...