how do you construct a 105-degree angle only using a compass and a straightedge?

Answer 1

I don't know the best way (fastest, least steps, that kind of thing), but here is A way:

1) Use the compass to make a useful length straight line segment. Call it Segment A.
2) Use the C&Se to bisect Segment A.
3) At its midpoint, found in 2), construct a perpendicular line segment whose portion that is above (or below if you prefer) is longer than Segment A. Call this Segment B.
4) Use the compass to draw an arc the length of Segment A pivoted on one of the endpoints of Segment A and long enough to cross the portion of Segment B that rises above Segment A.
5) Use the straightedge to draw a line segment from either end of Segment A to the point at which the arc crosses Segment B. Call this Segment C. The angle formed by Segment C and Segment A is 60 degrees. Call this Angle 1. Halfway, or so, there!
6) Construct a perpendicular to Segment C rising from the vertex of Angle 1 ("rising" away from all the other contructions so that the right angle formed and Angle 1 make a 150 degree angle). Call this Angle 2.
7) Bisect Angle 2. Call the portion sharing Segment C with Angle 1: Angle 3. Angle 3 is 45 degrees.
8) The combination of Angle 1 and Angle 3 is 105 degrees (60 + 45 = 105).

Answer 2

How To Construct 105 Degree Angle

Answer 3

Construct a perpendicular to a line... that makes 90 degrees.. You need another 15.

Now construct a 60 degree angle...
Put the point of the compass on the point where the perpendicular intersects with the line, and construct a quarter circle. Where the circumference of the circle intersects with the perpendicular, place the point of your compass and lay off the radius along that circle. That angle will be 60 degrees. (total 150 degrees)

Bisect the angle between the perpendicular and the angle just formed. That will give you 30 degrees. (total 120 degrees.... getting closer).

Again, bisect the angle between the perpendicular and the last bisection. That will give you 15 degrees (total 105).

Draw a line from the point where the perpendicular lines intersect to the last constructed point... the bisection. The larger angle so formed will be 105 degrees (by construction)

Done.

Answer 4

1. draw a straight line
2. pick some point along this line and use it as the center of a circle
3. draw another circle identical to that in 2 with its center on the same line only offset from the other
4. connect the intersection points of these circles which will give you a line perpendicular to the first that also intersects it
5. if you think of this as an x-y coordinate system and the intersection of the two lines as the origin, consider only the 2 quandrants where x is positive
6. in the bottom quadrant construct a circle using the intersection of the two straight lines as the center
7. use the intersection of this circle with the x-axis as the center of a second circle of the same radius and draw it in this same bottom quadrant.
8. connect the intersection point of these arcs with the origin. This line forms a 60 degree angle with the x-axis.
9. In the upper quadrant pick some point along the y-axis and draw a half circle starting from the origin (the radius of the circular arc is the distance from the point you picked to the origin)
10. using the same radius, repeat 9 only using the x-axis to position the center of the circle
11. draw a line from the intersection of these arcs to the origin. this gives you an angle of 45 degrees between the line and the x-axis.
12. combine angles from 8 and 11 to get the desired 105 degrees.

Answer 5

It won't be exact but...

The angle between north and east on the compass is 90*. So on a piece of paper draw a strait line and set the compass so the center of the compass is on the line. Turn the whole thing until the north arrow lines up with the line on the paper. Mark the east and west marks of the compass on the paper. Move the compass and draw a line between the east and west marks which should bisect the first line. The angle between the first and second line is 90*. So you need another 15*. 15 goes into 90 six times so divide the 90* angle into six equal pie pieces. Copy one of the pie pieces on the other side of the 90* angle and you will have a 105* angle.

Good luck!

Answer 6

Construct a right angle, then construct an angle of 60 adjoining it. Bisect the right angle, so that you have an angle of 45 next to an angle of 60. 60+45=105.

Answer 7

105=90+15

so first draw a 90 degree angle using a compass and scale.[hope u guys know]
after drawing it,then draw a 30 degrree and angle and bisect it to get 15 degree angle

see its very easy!!!!!!