Draw a 105 degree angle

- anonymous

Draw a 105 degree angle

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- mathstudent55

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- anonymous

it says using a ruler and a protractor @mathstudent55

- anonymous

in my hand :/

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## More answers

- Jhannybean

Just follow this video. https://www.youtube.com/watch?v=t4xCOUNEInI

- mathstudent55

I only see "Draw a 105 degree angle" above.

- anonymous

would you like me to re write the question ? @mathstudent55

- mathstudent55

No need.

- mathstudent55

Here's my way of doing it.

- mathstudent55

Start with a line, and mark two points on the line.
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- anonymous

okay ive done that

- mathstudent55

We are going to draw a square segment AB as a side.
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- mathstudent55

Open the compass to AB and center it at A and draw an arc.
Using the same opening, center it at B and draw an arc.
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- mathstudent55

Now we want to draw a perpendicular to line AB through point A and a perpendicular to line AB through point B.
Open the compass to any opening between AB.
Center the compass at A and draw and two arcs on line AB, one on each side of A.
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- mathstudent55

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- mathstudent55

Now open the compass more than AD, center is at C and center it at D and draw two arcs above A.

- mathstudent55

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- mathstudent55

Connect A to E and extend.
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- mathstudent55

FE is perpendicular to AB.
Also, FA = AB

- mathstudent55

Now open the compass to AB.
Center the compass at F and draw and arc to intersect the arc above B.
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- mathstudent55

G is the 4th vertex of our square.

- mathstudent55

We have square ABGF.
Since it's a square, all vertex angles are 90 degrees.
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- mathstudent55

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- mathstudent55

Now we extend line BG up above point G.
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- mathstudent55

Now we need half the length of the segment BG, so we draw its perpendicular bisector.
Open the compass to more than half of BG.
Center the compass at G and draw two arcs.
Then center the compass at B and draw two arcs that intersect the previous two arcs.
Connect the intersections of the arcs with a segment.
This segment is the perpendicular bisector of segment BG.
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- mathstudent55

GH is half of BG.

- mathstudent55

Open the compass to GH. Center the compass at G and mark a point above G on line BG.
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- mathstudent55

Sorry. I realize now I made a mistake when I tried to figure this out earlier.
We don't need half the side.

- mathstudent55

Let's go back to the square.

- mathstudent55

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- mathstudent55

Now we draw a diagonal in the square.

- mathstudent55

Since we constructed a square, we know each vertex angle measures 90 degrees.
Also, when we draw a diagonal, that bisects the vertex angle, so we have now two 45 degree angles at the vertex.
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- mathstudent55

We notice that 105 degrees = 45 degrees + 60 degrees.
If we place a 60 degree angle at that vertex, then 60 deg + 45 deg = 105 deg, which is what we want.

- mathstudent55

A 60-deg angle is not difficult to construct because it is the measure of the vertex angles of an equilateral triangle.

- mathstudent55

Now we construct an equilteral triangle at the upper left vertex of the square.

- mathstudent55

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- mathstudent55

Open the compass to AB and center at F. Draw and arc.
Then center at G and draw an arc.
Where the arcs intersect, it's the third vertex of equilateral triangle FGP.
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- mathstudent55

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- mathstudent55

Angle PFG measures 60 deg.
Angle GFB measures 45 deg.
Angle PFB measures 105 deg.

- mathstudent55

With the help of a square, its diagonal, and an equilateral triangle, we now have a 105-deg angle.

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