anonymous
  • anonymous
Draw a 105 degree angle
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
|dw:1440958077956:dw|
anonymous
  • anonymous
it says using a ruler and a protractor @mathstudent55
anonymous
  • anonymous
in my hand :/

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More answers

Jhannybean
  • Jhannybean
Just follow this video. https://www.youtube.com/watch?v=t4xCOUNEInI
mathstudent55
  • mathstudent55
I only see "Draw a 105 degree angle" above.
anonymous
  • anonymous
would you like me to re write the question ? @mathstudent55
mathstudent55
  • mathstudent55
No need.
mathstudent55
  • mathstudent55
Here's my way of doing it.
mathstudent55
  • mathstudent55
Start with a line, and mark two points on the line. |dw:1440958648016:dw|
anonymous
  • anonymous
okay ive done that
mathstudent55
  • mathstudent55
We are going to draw a square segment AB as a side. |dw:1440958758007:dw|
mathstudent55
  • 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. |dw:1440958818783:dw|
mathstudent55
  • 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. |dw:1440959091893:dw|
mathstudent55
  • mathstudent55
|dw:1440959116221:dw|
mathstudent55
  • mathstudent55
Now open the compass more than AD, center is at C and center it at D and draw two arcs above A.
mathstudent55
  • mathstudent55
|dw:1440959214600:dw|
mathstudent55
  • mathstudent55
Connect A to E and extend. |dw:1440959255726:dw|
mathstudent55
  • mathstudent55
FE is perpendicular to AB. Also, FA = AB
mathstudent55
  • mathstudent55
Now open the compass to AB. Center the compass at F and draw and arc to intersect the arc above B. |dw:1440959563117:dw|
mathstudent55
  • mathstudent55
G is the 4th vertex of our square.
mathstudent55
  • mathstudent55
We have square ABGF. Since it's a square, all vertex angles are 90 degrees. |dw:1440959604880:dw|
mathstudent55
  • mathstudent55
|dw:1440959655179:dw|
mathstudent55
  • mathstudent55
Now we extend line BG up above point G. |dw:1440959701330:dw|
mathstudent55
  • 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. |dw:1440959917480:dw|
mathstudent55
  • mathstudent55
GH is half of BG.
mathstudent55
  • mathstudent55
Open the compass to GH. Center the compass at G and mark a point above G on line BG. |dw:1440960034307:dw|
mathstudent55
  • 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
  • mathstudent55
Let's go back to the square.
mathstudent55
  • mathstudent55
|dw:1440960509048:dw|
mathstudent55
  • mathstudent55
Now we draw a diagonal in the square.
mathstudent55
  • 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. |dw:1440960561813:dw|
mathstudent55
  • 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
  • mathstudent55
A 60-deg angle is not difficult to construct because it is the measure of the vertex angles of an equilateral triangle.
mathstudent55
  • mathstudent55
Now we construct an equilteral triangle at the upper left vertex of the square.
mathstudent55
  • mathstudent55
|dw:1440960839669:dw|
mathstudent55
  • 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. |dw:1440960981941:dw|
mathstudent55
  • mathstudent55
|dw:1440961010150:dw|
mathstudent55
  • mathstudent55
Angle PFG measures 60 deg. Angle GFB measures 45 deg. Angle PFB measures 105 deg.
mathstudent55
  • mathstudent55
With the help of a square, its diagonal, and an equilateral triangle, we now have a 105-deg angle.

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